Dont wanna overthink it so ill go with the obvious choice which is Super Mario Bros. Presumably the game that saved gaming after the crash of 1983 while also putting the company in the map,

There is so many, that I have to say more than 1.  But I'm going to limit it to 5:

#5 Mike Tyson's Punch Out - This game is basically all boss fights, and the bosses are huge.  It had to have inspired games like Shadow of the Colossus and Dark Souls.  (Not to mention the "time it just right" then dodge/block then counter-attack gameplay shared with Dark Souls.)  At the end you fight the real life Heavyweight Champion of the World and he knocks you out in one punch just like if you really got punched by Mike Tyson.

#4 Super Mario Bros. - This is the first game I remember using music throughout the entire game.  The game also scrolled for the entire level.  (I remember Pitfall 2 doing a little of these things, but not to this extent.)  It has a crapload of secrets, and most importantly is how high the quality of gameplay was.  I remember feeling so powerful with the fireflower the first time I played this (which was in an arcade).  And also warp zones...there really are a lot of innovations in this game.

#3 Wii Sports - This game invented the entire genre of motion controls and became a huge cultural phenomenon bringing in many people who would normally not play video games.  I would love to see motion control games make a comeback, because I think Nintendo just scratched the surface of what was possible in this genre.  Wii Sports was amazing though.

#2 Donkey Kong - It's the first platformer that uses a jump button.  However, it's also the first game with a coherent story.  You see Donkey Kong carry Pauline up the skyscraper in the opening cutscene, an by the end of the 2nd stage Mario makes him fall down and saves Pauline.  It actually is a more coherent story than the one you experience while playing Super Mario Bros. not to mention a whole lot of other games.

#1 The Legend of Zelda - This is the game that killed the arcades.  It took several years, but this is the game that made it happen.  The gameplay of Zelda 1 was not possible in either an arcade or a home computer at the time.  You needed to be able to save your progress, which was something arcade games couldn't do.  And the game was too twitchy for any home computer in the mid 80's.  It's the first action RPG, taking Ultima 1 gameplay, but then making it an action game.  It also took the item ideas from Adventure and then took them so much further too.  The game has tons of secrets.  It's the first open-world action game.  The game overworld feels huge compared to any action game that came before, and it has 9 dungeons.    

Zelda 1 just went so far and beyond every similar game that came before it, and since you could only experience this type of game on a home console, it ended up killing the arcades.  That is why I put it as Nintendo's #1 most revolutionary game of all time.  A true revolution has to overthrow the existing status quo, and that is exactly what it did.  Gaming used to be defined by arcades, and even the best selling games on the Atari 2600 were mostly arcade ports.  Zelda 1 showed you could make home console games that were a bigger draw than anything that was possible in the arcade.  Zelda 1 shifted gaming from games made for arcades to games made specifically to be played on a home console.

Yeah, someone would have made a jump-based platformer eventually but would it have had an impact on the industry like Donkey Kong made?  And you could argue that Nintendo, like everyone else, has been inspired by others' ideas too, particularly by Namco's:

Space Invaders inspired game:

Galaxian - Namco, 1979 / Radar Scope - Nintendo, 1980

Mascot in a game:

Pac-Man - Namco, 1980 / Donkey Kong - Nintendo, 1981

Mascot in a 2D side-scroller:

Pac-Land - Namco, 1984 / Super Mario Bros - Nintendo, 1985

Obstacle based fighting game:

The Outfoxies - Namco, 1995 / Super Smash Bros - Nintendo, 1999

With Donkey Kong though, I don't see an inspired idea in a game before 1981 that was built upon from a gameplay standpoint.  Nintendo also beat Namco to the mascot kart racer but they found mutual ground eventually. 

Yeah Wii Sports would be one of my picks too.

There's a lot of revisionist history where those who didn't like motion controls/the Wii claim that it's breakthroughs went nowhere, but I'd argue that it did more than almost any other single game this century to open up gaming to new audiences, growing the "casual" market who make up a large presence to this day on mobile/PC and on Switch/2, helping propel the success of games like Animal Crossing New Horizons, Ring Fit Adventure, etc.

As a Zelda fan, I have to disagree with few things here:

- arcades were already in downward spiral by the time Zelda released...Golden Age of Arcades ended around '83, due to both home consoles and home computers

- games made for home VG entertainment were already quite different than just being arcade ports way, way before Zelda (especially on home computers)

- home computers were more than capable of Zelda's action gameplay and already had quite a few games that were twitch based, while not being arcade alike in structure (proto-Metroidvania, "Montezuma's Revenge" from '84 comes to mind).

- while you'll never catch either Miyamoto or Tezuka admitting it, Hydlide did exist before Zelda (on home computers, no less). Is LoZ better game? Sure. Is it first? No.

Zelda is continuation and distillation of what was happening on home gaming devices already for years prior to it. It is one of the seminal titles in gaming history, but I find it that lot of people are looking at it with too much rose tint in their glasses.

From my POV, nothing really compares to Donkey Kong, which made Nintendo (and saved NoA) into VG juggernaut...that Radar Scope cabinet was doing pretty bad, and DK came as last ditch attempt to salvage it, massively succeeding and in the process codifying new type of gameplay.

that is true, but to be fair, some do claim "it would never have happened" which is a wild jump.  Like that one discussion where someone claimed we would still have d-pads only in 2026 if not for N64.  I mean those claims are such a stupid claim, it blows my mind.  

But yes, the first to do something get credit, as does someone who standardizes something that already exists, like dual analog via Sony.

Edit

If you look at history, before global travel was readily available, many cultures developed technology around the same time.  I can't tell you how many times i have beaten the competition to patents by a few months.  Dual development is a real thing.

Agriculture was developed independantly in the Fertile Crescent, China, Mesamerica and Andes. 

the "never would have happened" argument is (frankly) horse****. 

I fully agree.  I think a lot of the Wii fans skipped the Wii U, but came back for the Switch.  Mario Kart Wii sold more than any Mario Kart that came before, and it had motion controls.  Then Mario Kart 8 comes along and blows away MK Wii in sales.  Mario Kart 8 also has motion controls.  Those Just Dance games keep selling too.  The motion control audience is still there.

And speaking of revisionist history...

"- arcades were already in downward spiral by the time Zelda released...Golden Age of Arcades ended around '83, due to both home consoles and home computers"

Gradual decline?  Yes.  Downward Spiral? No.  Arcades were still doing well even after the home console market crashed in the US.  This was the biggest indicator to Arakawa, President of NoA at the time, that the NES would be successful in the US.

"- games made for home VG entertainment were already quite different than just being arcade ports way, way before Zelda (especially on home computers)

- home computers were more than capable of Zelda's action gameplay and already had quite a few games that were twitch based, while not being arcade alike in structure (proto-Metroidvania, "Montezuma's Revenge" from '84 comes to mind)."

Just watched a video of Montezuma's Revenge.  The controls look clunky as hell.  Action games on home computers were not good in the 80's. That detail matters a lot.  Gameplay on home consoles was much more fun for action games.  The release of the NES killed Commodore.  It released the Amiga, which was clearly better than the C64, but it didn't sell like it.  Why?  The C64 had no competition from consoles while the Amiga had to compete with the NES. 

"- while you'll never catch either Miyamoto or Tezuka admitting it, Hydlide did exist before Zelda (on home computers, no less). Is LoZ better game? Sure. Is it first? No.

Zelda is continuation and distillation of what was happening on home gaming devices already for years prior to it. It is one of the seminal titles in gaming history, but I find it that lot of people are looking at it with too much rose tint in their glasses."

A) Hydlide sucks.  And yes, quality matters.  If the game sucks then it really doesn't matter.  This is why the Power Glove is a joke instead of getting credit for inventing motion controls.  The Power Glove actually did motion controls long before the Wii remote did.  But the Power Glove sucked.  Quality matters.

B) Most importantly, you missed my overall point.  The NES created a new paradigm for gaming compared to what came before, and the game that started this paradigm was Zelda 1.  The previous paradigm was that the arcade was the main venue for gaming.  The best games were at the arcade, and most of the top selling Atari games were arcade ports.  Super Mario Bros and Duck Hunt were very popular early NES games, but they were also arcade games.  The first popular NES game that was made specifically for the home was The Legend of Zelda.

And the popularity of Zelda matters, because after Zelda 1 released the NES (and all following consoles) made more and more games specifically for home consoles.  The main venue for gaming became the home instead of the arcade.  The popularity of Zelda matters, because it ended up changing everything that came after it.  Games like Mega Man, Dragon Quest, Final Fantasy, Metal Gear, Super Mario Bros 3, etc... are all NES games made specifically for home consoles not to mention the many, many games that followed on later consoles.  The NES created a new paradigm for gaming and the pivot happened when The Legend of Zelda released.  That's why it is the most revolutionary game Nintendo (or anyone else) ever made.  Zelda started the revolution that made home console gaming overthrow arcade gaming.

• (Microsoft) Adventure? 1976, Apple II version 1979: https://en.wikipedia.org/wiki/Microsoft_Adventure
• Zork? 1977, Apple II version 1980
• Voodoo Castle? Apple II version 1980
• The Count? Apple II version 1980
• Mystery House? Apple II version 1980
• The Wizard and the Princess? Apple II version + Atari 8-bit version 1980
• Ghost Town? 1980, Apple II version + Atari 8-bit version early 1981

No, Zelda 1 was NOT the "first action RPG": https://en.wikipedia.org/wiki/Action_role-playing_game

No, Zelda 1 was NOT the "first open-world action game":

• https://en.wikipedia.org/wiki/Mercenary_(video_game)
• https://en.wikipedia.org/wiki/Hydlide
• https://en.wikipedia.org/wiki/Elite_(video_game)
• https://en.wikipedia.org/wiki/Open_world

And why was the gameplay of Zelda 1 "not possible" on any home computer of the mid '80s? "Too twitchy"... yeah, right! The NES hardware did nothing, a Commodore 64 couldn't do and in the mid '80s even Atari ST and Amigas already launched.

Donkey Kong, Super Mario Bros. and The Legend of Zelda have more than enough game elements and accolades to praise them... you don't have to add false facts to praise them even more!

Is it really so hard to write "one of the first open-world action games" instead of "the first open-world action game"?

I just wanted to write "Bollocks mate", but since you're half a decade or so younger than me and you obviously lack first hand experience in some areas from  80s, let's unpack some of your answers:

""- arcades were already in downward spiral by the time Zelda released...Golden Age of Arcades ended around '83, due to both home consoles and home computers"

Gradual decline?  Yes.  Downward Spiral? No.  Arcades were still doing well even after the home console market crashed in the US.  This was the biggest indicator to Arakawa, President of NoA at the time, that the NES would be successful in the US."

Arcades were declining steeply after '82, and went from $8B in '82 to $1.2B in '85 in the US. Were they dead? No. Especially not in Japan and the rest of the world. But in US they were at their lowest before NES even launched, so bollocks mate - no, NES didn't killed arcades, which is what you originally claimed. They actually went slightly up after '85 due to occasional games like Outrun and Double Dragon, to hit new peaks during early 90s with fighting games. What later "killed" arcades in US (and eventually everywhere else) were home 3D gaming systems, not NES.

""- games made for home VG entertainment were already quite different than just being arcade ports way, way before Zelda (especially on home computers)

- home computers were more than capable of Zelda's action gameplay and already had quite a few games that were twitch based, while not being arcade alike in structure (proto-Metroidvania, "Montezuma's Revenge" from '84 comes to mind)."

Just watched a video of Montezuma's Revenge.  The controls look clunky as hell.  Action games on home computers were not good in the 80's. That detail matters a lot.  Gameplay on home consoles was much more fun for action games.  The release of the NES killed Commodore.  It released the Amiga, which was clearly better than the C64, but it didn't sell like it.  Why?  The C64 had no competition from consoles while the Amiga had to compete with the NES. "

It is obvious you have no experience with C64 if you're claiming this, so bollocks mate. Is NES better gaming system than C64? Yes, gaming was its main purpose and it launched later. Is C64 capable of smooth action gameplay, like in LoZ? Absolutely.
And Amiga (being completely irrelevant for this issue) didn't compete with NES, but with Genesis ans SNES, at vastly higher price.

""- while you'll never catch either Miyamoto or Tezuka admitting it, Hydlide did exist before Zelda (on home computers, no less). Is LoZ better game? Sure. Is it first? No.

Zelda is continuation and distillation of what was happening on home gaming devices already for years prior to it. It is one of the seminal titles in gaming history, but I find it that lot of people are looking at it with too much rose tint in their glasses."

A) Hydlide sucks.  And yes, quality matters.  If the game sucks then it really doesn't matter.  This is why the Power Glove is a joke instead of getting credit for inventing motion controls.  The Power Glove actually did motion controls long before the Wii remote did.  But the Power Glove sucked.  Quality matters."

No, Hydlide doesn't suck. For its time it was fairly innovative (along with few other like it). Is LoZ better? Yes. Is it first do to what games before it already did? No. Thus, bollocks mate to your "first open-world action game".

"B) Most importantly, you missed my overall point.  The NES created a new paradigm for gaming compared to what came before, and the game that started this paradigm was Zelda 1.  The previous paradigm was that the arcade was the main venue for gaming.  The best games were at the arcade, and most of the top selling Atari games were arcade ports.  Super Mario Bros and Duck Hunt were very popular early NES games, but they were also arcade games.  The first popular NES game that was made specifically for the home was The Legend of Zelda.

And the popularity of Zelda matters, because after Zelda 1 released the NES (and all following consoles) made more and more games specifically for home consoles.  The main venue for gaming became the home instead of the arcade.  The popularity of Zelda matters, because it ended up changing everything that came after it.  Games like Mega Man, Dragon Quest, Final Fantasy, Metal Gear, Super Mario Bros 3, etc... are all NES games made specifically for home consoles not to mention the many, many games that followed on later consoles.  The NES created a new paradigm for gaming and the pivot happened when The Legend of Zelda released.  That's why it is the most revolutionary game Nintendo (or anyone else) ever made.  Zelda started the revolution that made home console gaming overthrow arcade gaming."

Distortion field at its strongest (along with general lack of knowledge of gaming history). Way prior to LoZ there was an action game that was very different from arcades that sold exceptionally well on previous gen console that showed that you can have action games that are not just arcade ports or arcade alike (what's funny is that you even mention it) - yes, Adventure on Atari 2600. Not to mention all other games from that time that were very different from arcades, and different at that in lot more ways than LoZ ever was.

LoZ is one of the most influential games of all time. Most revolutionary ever made? Pure bollocks mate.

Few things disrupted the gaming industry as much as Wii Sports.

I would love to say DK, SMB or LoZ, but the answer to this question is Wii Sports.