Hard to decide.
Last gen (last decade) was about open worlds, online gaming, being, cover based shooting. I'd want a list defining this decade to feature 8th gen machines and what they brought to the table. Not my five favorite games but games that embody the last ten years.
Here goes:
-Fortnight: Free to play social gaming with tons of DLC and (I guess) loot boxes.
-Minecraft: Creativity and social aspects
-Super Mario Odyssey: Full featured home experience on the go.
-Hollow Knight: Indie games that are better than most big studio games
-No Man's Sky: Overhyped games that launch incomplete but become great later on

Wanted to mention a VR game too. Honorable mention to Astrobot, I guess.

I don't care if it's not a "scientific article," that doesn't mean you can just make stuff up and present it as fact just because you want it to be true.  If you do, don't be surprised when someone asks you for a source. 

This is gonna be a bit long, but whatever, im feeling positive today, and im taking the “for you” part of the OP quite literally, so here goes a lot of praise to games I loved and defined the decade for me

Honorary mentions: Hollow Knight, Breath of the Wild and Pokemon XY and 30+ games because it was a good decade

5.- Witcher 3 (1 pt)
4.- Monster Hunter World/Iceborne (2 pts)
3.-  The Last of Us (3 pts)
2.- Bloodborne/Souls series (4 pts)
1.- Nier Automata (5 pts)

Honorary Mentions:
 Breath of the Wild cause I love it. Whats there not to love? And while I don’t put it in a pedestal like many  people here do, I still find it to be a very rewarding and fun experience. I just put it the 30^th spot of my top 50 games thread so, its up there with the big guns. Much love for this game. I'd say this is the average gamer's favorite game ever, but I mean it as a figure of speech, so dont take it quite literally and expect scientific data on this. 

Pokemon XY for the simple reason that its like a self-aware Pokemon game, it knows its characters and story are shit and doesn’t bother making you waste time with them and GOOD. I rather it not waste my time like Sun/Moon and Black/White did. Im here for the competitive team building and no Pokemon game defined better than XY. Best pokemon game since Gold/Silver for me and unlike – ehem – certain entries, it has much more than just 400 mons.

Hollow Knight – Its Hollow Knight, like, what else do you want. Its Hollow Knight, It’s the perfect indie game/metroidvania, its called Hollow Knight. What else do you want.  Play it. Also its amazing.

Witcher 3 for the simple fact that it mixes superb story telling with superb visuals with superb gameplay and superb world building. It gets either a 9 or a 10 in every category  you can analyze about a videogame (for me, don’t @ me if you disagree) and its by far the best open world RPG game ever created.  Rightfully it has the record for most GOTY won ever (Didn’t fact check, but I think its still got it) and its all in all a fantastic game and experience. I’d argue that neither Skyrim nor BOTW reached this degree of craftsmanship for the open world genre. Except I wont argue that because don’t @ me.

Monster Hunter World – Because I fucking love me some Monster Hunter. Underrated franchise, even if this particular entry was VERY successful. It was about time it broke through in the west. I love the gameplay, the grinding, I’ve invested over 300hrs into MHW/Iceborne and im still playing it. Its VERY fun in a manner I hardly find in other games. Not even MK8 – and I love MK8 – gets me so invested in its gameplay.  Fun.  Simple as that.

The Last of Us – Story is important for me. Secondary to gameplay perhaps, but still important.  A good narrative/story elevates a good gameplay. Every aspect of a game counts, and narrative driven games like the ones Naughty Dog develops are a goldmine of enjoyment for me. I love every Uncharted, even if U1 feels dated now and I absolutely love TLOU. Its fun, scary, grounded, has great characters and an amazing ending . It was an instant classic when it came out and Im very much looking forward to TLOU2.    

Bloodborne – Im really thinking of the whole Souls series here but as far as im concerned Bloodborne is the best it has to offer. Best lore, best world setting, best art style – and specially – best gameplay. I love me some Bloodborne. I have squeezed everything I can from this game and enjoyed it and very few games make me wanna do that. I love the Souls series and I specially love Bloodborne.  Sekiro not included.

Nier Automata – I know it’s a weird choice for some of you, but no game of the last decade that I can think of as of right now hooked me up with its story, pacing, music, intensity and gameplay like Nier Automata did. I wasn’t expecting it to be that great. I personally think its better than Nier and Drakengard (Both great games, im not talking shit about them).  It might not be the best looking game graphics-wise, but I loved everything about it.  

Don’t  @ me. Ill maybe edit later and add like 42 honorary mentions and make this post longer because life is like that sometimes and theres nothing we can do about that.

That's okay.  I'm sorry about your view of the gaming landscape, too.

Yep. 2007-2013 pretty much saw JRPGs regulated to handhelds. Persona was the only series carrying the torch of good console JRPGs at the time (but even then it was a PS2 series, in a 360/PS3 era). I loved Ni No Kuni, and bought the sequel, but have yet to play it. 

In many ways, I haven't really liked this decade. Gaming-wise, there haven't really been many decade-defining games for me this decade. That's actually only two games. The rest on my will definitely stay in my mind but there's really only two decade-defining games, and even they pale in comparison to Metal Gear Solid 2 and Final Fantasy X from the 2000s. Anyway, on to the list!

1. osu!

There's just so many wasted hours here almost daily from 2012 up until this day and until foreseeable future. osu! is probably more like a lifetime-defining game than a decade-defining game, whether I like it or not. I was going through a fairly difficult period in my life when I got into osu!, and it's a great game too.

2. Minecraft

Perhaps Minecraft isn't all that innovative, but it was definitely the game that popularized whatever it is that it's doing. I've played Minecraft much less than I would have liked, and I have certainly played it quite a bit. Playing Minecraft isn't the only way to consume it though; There's also YouTube, which I've almost certainly spent much more time on (in the context of Minecraft) than playing the game. Like osu!, Minecraft really stands out from the rest.

3. The Elder Scrolls V: Skyrim

The problem with Skyrim is that it's even that great a game. However, it's impossible to downplay how big it is and how prevalent it is in the decade.

4. Metal Gear Solid V: The Phantom Pain

Had MGSV been just another game in the series, it probably wouldn't have ended up on my list - mainly due to clearly being unfinished. (It's still a great game even as it is though.) However, it's Kojima's last MGS game, which makes it stand out much more. It's the end of an era, which is why it deserves a place on my list.

5. Grim Dawn

Titan Quest was huge back in the day, and come to think of it, due to the amount of Titan Quest I've played this decade, perhaps Titan Quest should be the one on my list. However, my love for Titan Quest came to existence during the previous decade, so it wouldn't fit all that nicely on this list. Instead, I'll choose its spiritual successfor: Grim Dawn. Again, I've played Grim Dawn much less than I would have liked, but due to Titan Quest's legacy, it's quite special for me.

I had two strong contenders in addition to these five: Rocket League and Cities: Skylines. Rocket League is currently my most played game on Steam, and Cities: Skylines is also among my most played games. I also would have liked to have them on my list, but I strongly suspect that time will pass by them and they won't stay in my mind the way the five games I've listed have. Then again, only the top 2 games from my list really defined the decade for me, so including even more games would simply have been wrong.

This is rather hard.

1 - Mount and Blade: Warband = My dream game in this flawed, flawed game. (5p)
2 - The Legend of Zelda: Skyward Sword = This was an endurance test. I finished the night before the Switch and Breath of the Wild arrived. (4p)
3 - The Legend of Zelda: Breath of the Wild = There's still more to play, the save file went poof, when my Switch died. I got it fixed for free though... (3p)
4 - Total War: Shogun 2 = My long road into Total War madness begun here and ended with Warhammer 2 and I'm done forever now. (2p)
5 - Broken Sword 5 = I fell in love with this series and it brought me back into Adventure games. (1p)

Honorable mentions: The Elder Scrolls 5: Skyrim would be 6, Super Smash Bros. Ultimate, Sushi Striker, Velocity 2X, Disgaea 5, Captain Toad's Treasure Tracker, Tropico 4, Endless Space, Splatoon 2, Mario Kart 8 Deluxe, Samurai Warriors: Chronicles, Pokemon Sun, Metroid 2: Samus Returns, Super Mario Odyssey & Valkyria Chronicles 4 (still playing through it.)

5. Grand Theft Auto V - The game that just keeps on selling. The biggest, most successful title in Rockstar North's history. One that shatters the previous limits and expectations of GTA titles.

4. Overwatch - During a time where the FPS genre was getting over-saturated and stale with the same style and approach. Overwatch provided a huge breath of fresh air and a unique spin on a genre that was stagnating at the time of its release. And it has managed to maintain its popularity and become a big-time money maker for Blizzard.

3. Fortnite - If there's one genre/style that exploded in popularity in the latter part of the decade, it's the "Battle Royale" style and there was no other game that was more popular in this style than Fortnite.

2. The Legend of Zelda: Breath of the Wild - Nintendo did it again. At a time where the future of their hardware business was called into question. They needed the Switch to launch with a game-changing killer app that would send it skyrocketing. That's exactly what Breath of the Wild did. Shattering bars and changing the landscape of the Zelda series while showing just what portable/hybrid gaming was capable of. To this day, for me, this is still the Switch's best game and signature title.

1. Minecraft - Easily the most popular game to come out of this decade. What Tetris was back in the 80s, Pokemon Red/Blue in the 90s, and Wii Sports in the 00s, Minecraft was for this decade. A game that went on to become a phenomenon and become not just a big part of gaming but also popular in pop culture as well. Pretty much every kid, teenager, and young adult today knows what Minecraft is. A top seller in just about every system the game is on.

So the ones I believe defined the gen:
1. The Legend of Zelda Breath of the Wild (5 points), yes I'm a Zelda fanboy.
2. Minecraft (4 points)
3. Fortnite (3 points)
4. TES Skyrim (2 point)
5. Dark Souls (1 points)

Minecraft.