Interesting, good list, but I have some major disagreements. Mostly because I disagree with the criteria and how they are weigthed. I don't see why current popularity is weighted so highly, compared to historical popularity, when you are rating greatest franchises of all time, not as of now. I would argue Pong and Doom dominated the market a lot more in their prime than current trendy games such as PUGB, Lol, Fortnite. But also my criteria would be completely different.

First off I would disqualify games that are only/mainly based around online multiplayer for the following 3. reasons:

1. I see video games as an art form first, but most (not all) online multiplayer games are more sport than art.

2. For something to be the greatest of all time, it needs to have some sort of timeless relevance. Future generations won't ever get the Fortnite experience, because it either literally won't be playable or they won't have the option to experience it with the number of players that make the experience great in the first place.

For the same reasons, the online component of games with both offline and online content will not be evaluated.

My other criteria would be:

-Overall critical acclaim

-At least three separate critically acclaimed and popular games to make it a proper franchise

-Historical/cultural impact and influence

-The franchise's ability to reinvent itself and draw in new audience with new releases

-Historical consistency: If acclaimed games span several generations, it is a plus

-Legacy titles remain popular/relevant even after release of newer titles

-The more 'great' games the franchise has, the more likely it is to rank high

With these criteria, the top 10 franchises would be:

1. Mario platformers  - With the exception of gen 1 and 6, each gen has had at least one Mario platformer that made the top 10 most acclaimed games of that gen.

2. The Legend of Zelda  - Every generation from the 3rd onwards has had a Zelda game in the top 15-20 most acclaimed games

3. Metal Gear - Every generation from the 5th onwards has had a Metal Gear game in the top 20 most acclaimed games, and even the games before that were somewhat acclaimed

4. Doom - Not as many games as some other franchises, but the consistency, longetivity and influence makes it high on the list. DOOM (1993) is obviously the most important, and while the follow-up games in the 90s were "more of the same" they are still games with sustained popularity. DOOM 3 might be divisive, but the impact on game design when it comes to graphics, sound and atmosphere is often understated. DOOM (2016) and DOOM Eternal basicly reinvented the modern shooter.

5. Resident Evil - It had some bad years during the 7th gen, but has otherwise remained consistent among the most acclaimed series and the most important in the horror genre

6. Grand Theft Auto - The influence is enormous and the critical acclaim is consistently high, the only reason it is not higher is because all the relevant games were released in the span of just 12 years (2001-2013), GTA VI would need to match previous titles for the series to climb higher.

7. Final Fantasy - Obviously peaked in the 90s and early 2000s, but the acclaim and popularity of VII remake and XVI cements its spot.

8. Sonic the Hedgehog -Controversial probably. While it certainly peaked in the 4th gen, where it was probably the most important franchise, it has reinvented itself many times since, sometimes more successful than others. It certainly sustained its relevance into the Dreamcast era with the Adventure games (though I dislike them personally), and games like Colors, Generations, Mania and Frontier have shown that it can still deliver good new experiences from time to time.

9. Castlevania - Extremely important in the 80s and 90s. GBA-DS titles are also highly regarded. Unfortunately it has kind of disappeared.

10. Metroid - Major gaps between releases, but once it shows up, it is usually an event.

Honorable mentions:

Halo - Very relevant during 6th and 7th gen, been in decline since.

Call of Duty - Black Ops 2 was probably the last title that had some sort of timeless relevance, as each title since seems to disappear from the discourse once the sequel arrives. But those 7th gen titles certainly left an impact.

Assassin's Creed - Last truly loved title was probably Black Flag, but I guess the series has managed to reinvent itself, for instance with Origins. The franchise is still "young", so perhaps with a return to form, it can climb the ranks.

Pokemon - It has not managed to reinvent itself or expand to a broader audience, except when it comes to Pokemon Go, which almost made it break the top 10 here. Still last Gen 2 was probably the last time it delivered a game-of-the-generation contender. But the series has remained consistent over the course of many entries.

God of War - It is on its way, but probably needs to come up with something "new" once more.

Mega Man - Used to be extremely important, and I guess it has been consistent to this day, but it has become a "small" franchise.

Street Fighter - The problem with fighting franchises, is that there are usually only 1-2 games that stay relevant. Street Fighter is the closest to an exception, as II, III, IV, Alpha 2, Alpha 3 all remain somewhat popular. However, they are still quite similar.

Fortnite has mobile. Didn't you know that?

Could say that monster hunter is knocking on the door of the top 10. Both world and rise have really elevated the series popularity

It does? I thought Apple and Google removed it

Current popularity is not weighted highly. I'm rating the popularity appropriately by accounting for the world population at their respective time and the size of the gaming market. Doom and Pong may have dominated their "platform", but the numbers are significantly smaller, even accounting for the factors stated above. I think the bias is getting you. When we talk about the history of games, do you really think we can ignore the impact of some of these multiplayer games? This isn't a top 10 single player, this is top 10 including EVERYTHING. I respect your list because you have all of my favorite franchises in there, but that doesn't mean it's valid imo.

If we did that, then we wouldn't be talking about franchises, because an "IP" can literally just be a single game.

Now, if we talked about the top ten games of all time based on similar criteria I listed before (e.g., impact on the industry, importance to gaming history, still enjoyed years after its release, long-term cultural relevance), the list might change up a bit, but it would consist mostly of older titles. Just to give a list of definite titles or strong contenders I would or might include in a Top 10 list, it would be (in release order; definite titles bolded)

Pac-Man
Super Mario Bros.
Tetris
The Legend of Zelda
Sonic the Hedgehog
Doom
Street Fighter II
Mortal Kombat
Final Fantasy VII
Pokemon Red/Green/Blue
Grand Theft Auto III
Halo CE
World of Warcraft

Now, I might be a bit more inclined to include games like League and Fortnite in such a list. Probably not in the Top 10, but likely in a Top 20. League has been popular for over a decade now, it popularized MOBAs, and it's a huge e-sport. Fortnite was, along with PUBG, instrumental in popularizing battle royale games & game modes. Hard to say if the popularity of those games or their genres will remain, especially with something as relatively new as Fortnite and BR games.

One thing that's always bugged me about a lot of Top 10/20/30 "Greatest ___ of All-time" lists, especially when its just regular people voting, is the recency bias. So often these lists are inundated with recent titles that were really popular and/or acclaimed, but just because a game is popular now doesn't necessarily mean it will have the kind of long-term impact on the industry or the staying power of a certified classic like Super Mario Bros. There is a lot of well-regarded science fiction cinema and TV still being released, but how much of it, regardless of quality or current popularity, will be remembered 30+ years later in the same breath as classics like Star Wars, Star Trek, E.T., Blade Runner, Alien, or 2001: A Space Odyssey?

Also, a lot of popular games released over the past 5-10 years are free-to-play, which I would consider a huge caveat. Would they have been as popular if they were premium $60 titles instead of games that let players in the door at no charge and then try to squeeze money from them after the fact with microtransactions and seasonal DLC? Even if the game is legitimately fun for those that play them, I imagine the negligible barrier to entry is a huge factor. Some of them have remained popular for years now, but what about in another decade or two?

For example, Fortnite has been steadily bleeding population for the past couple of years, and while the remaining population is still high, if it continues on this path it could gradually fade away. If the game stops being profitable for Epic, they'll eventually just shut it down, and nobody will get to play it ever again (the eventual fate of every always-online game). While the game will probably be well-remembered by those who played it in its heyday, and it did result in the popularization of battle royale games (which may not stay popular forever; not only is Fortnite possibly past its peak, but PUBG has only a fraction of the players it did in 2017, and it seems to continually lose players), there's reason to be skeptical at the moment that it will be remembered decades later in the same way so many other classics have.

If you had made those adjustments, Pong would certainly rank higher than Fortnite, Pong alone had a majority market share. A whole generation of game consoles were designed to play that game. Granted, Pong does fail on some of your other criteria.

Based on your criteria though I would probably still take PUBG and Fortnite off and replace with Warcraft and Counter Strike (alternatively Street Fighter), then the list is pretty accurate (depending on the definition of a franchise though).

My list is biased, not in the sense that these are my 10 favorite franchises (they are not), but in the sense that I look at games as an artistic medium, and competitive games are just something else that cannot be compared to other games. It would be like having a list of greatest TV shows and throwing the Fifa World Cup in there. It just doesn't make much sense to me. Apples and oranges I guess.

And then as I mentioned, these online focused games will eventually fail completely on longetivity, as they eventually become unplayable.

Since when are PUBG and Fortnite franchises? They're both at exactly one title so far. Also, why isn't FIFA a game franchise in your eyes?

1. Pong did have majority of market share at the time, but the market was miniscule. I doubt there was even 10 million people that experienced the game out of estimated 3 billion people on earth at the time. Fortnite has more than that from this month alone. The circumstances are different, one is f2p and the other is p2p, online play and offline, etc. so the amount of player Pong had is not equal in value to the amount of player Fortnite has. However, even accounting for all of this, Fortnite accomplished much more.  Like I said in my previous posts, Subway Surfers is the most downloaded game ever, but because I accounted for all of the things stated, it will never get a spot in the top 10. I took all the points into consideration mentioned in the op. We can't ignore the massive success from these newer IPs. Arcade to Consoles to PC to Mobile to VR, offline to online, old to new. They are all different, but they are all inside the category of video games. 

2. Your TV shows to Fifa World Cup analogy isn't accurate because my list excludes IPs that didn't originate from video games. This was brought up at the beginning of the forum. Fifa has one of the most popular games out there, but I didn't include it for that reason. If there was a list of greatest TV shows, then it would be strictly to TV show not a sport event like Fifa World Cup.

You look at games artistic, maybe the disagreement comes from that. Historical art are rated significantly higher from art enthusiasts. I personally think there are better modern digital art out there, but those will never be rated highly from them. Before we bring up AI art, I want to make it clear, that's very different as of today because AI art is like stealing assets in video games. My perspective is "art is art", so it should be viewed equally digital or not. If a digital art expresses creativity on the same level, then it should be considered a masterpiece nonetheless. I know some things are easier to do digitally, but that's what evolution does. Things get better, quality and QOL improves as we go. I think you view them as different things, that it should never be compared. The problem with that is where should we draw the line. Artists had different tools and environment for physical paintings as well. Game developers having to work with different platforms, should we just not compare them at all? 

3. It hurts me to say this because I love single player games more and I'm not a fan of this live service stuff, but these online focused games are staying relevant than most single player games. Mainly because they have the advantage of getting new content every month through updates. You do have a point that live service games can become unplayable when servers are shutdown, but similar things can be said with older games since they can break. Nothing is permanent. 

That's something that was brought up constantly and I don't blame you for not being caught up. But essentially it's because both PUBG and Fortnite are IPs that constantly generate revenue for the publishers due to it being live-service that constantly adds content to keep consumer interest.

Fortnite has Fortnite: Battle Royale, Fortnite: Save The World, and Fortnite: Creative. 
PUBG has PUBG mobile, PUBG splash royale, PUBG new state, etc.

Definition of a franchise - an authorization granted by a government or company to an individual or group enabling them to carry out specified commercial activities

Both PUBG and Fortnite does this e.g. Krafton licenses their IP to Tencent for PUBG mobile, Epic license for Fortnite merches. 

However, to avoid confusion it should be top intellectual properties instead of franchise I suppose. 

FIFA isn't a game franchise because The Fédération Internationale de Football Association (FIFA) originated before the game. FIFA licenses their brand to EA, that's why "EA Sports FC 24" exists now because FIFA and EA couldn't come to a license agreement.