Witcher III - Probably doesn't really deserve to be on the list, way to recent, and it more a culmination of trends rather than a trend setter.
Baldur’s Gate 2 - Haven't played it, but as a long time cRPG fan I'm well aware of it's impact. To this day cRPGs are compared to it and said to be it's spiritual successor. The level of writing quality is perhaps the peak of old Bioware and the game, to my understanding, is generally considered a masterpeice. Those saying to replace it with ME2 are giving into modernity bias, as the writing of ME2 is by far inferior to many earlier titles (I encountered better writing in Dragon Age: Origins, Neverwinter Nights and all its expansions, and if we leave Bioware for a moment: Planescape: Torment, and Neverwinter Nights 2: Mask of the Betrayer, Fallout 2, and many more all featured better writing and characters than ME2.)
Minecraft - Definitely deserves to be on the list. Launched a new genre of games and is still massively popular.
Diablo II - Those of you who haven't played it or are younger don't really grok how important this game was. Not only is it to this day the definitive action RPG, but it pioneered online play and netcode, along with being one of the first M games that really lived up to the title and used it for more than shock.
Half-Life 2 - Yeah... not seeing it. It didn't do much new in the FPS genre and while it was graphically impressive and had a unique physics engine, it... was more a flash in the pan.
Counter-Strike - Yeah, this one does deserve to be on the list. For those who don't know Counter-Strike basically invented the modern realistic FPS arena team shooter. Prior to this arena shooters were primarily based on Unreal Tournament with its fast bouncy gameplay and utter lack of realism. Counter-Strike changed all that.
Elder Scrolls V - A great game to be sure, and while it's longevity is held up by mods, I'm not sold on it being on this list. That said, at this time it IS the definitive sandbox RPG so perhaps it does belong here.
Civilization - Agree with those who'd swap it out for the sequel Civilization 2. While it launched the genre, I feel that Civ2 is the best and most influential example of it.
Portal 2 - While narratively good and an impressive sequel, I'm not seeing it. As far as puzzle platformers go it's good, but again, it's a flash in the pan.
Fallout: New Vegas - I can understand BG's case for Fallout 3 deserving to be on here over NV. Honestly, with Skyrim on here I feel that neither Fallout 4 or NV really deserve to be on here as they're just a setting swap of the open world RPG formula.
Doom Eternal - Not played it or Doom 2016. To be frank though I feel neither belongs on this list, if you want a representative of the Doom franchise, the original Doom really should be here, as it was one of the major genre defining FPS (which, for a long time, were called "Doom Clones") and had much greater impact than either of the two modern Doom games. So yeah, replace this with OG Doom.
World of Warcraft - Yeah, I can see this. It is the definitive themepark MMO and still potentially one of the biggest MMOs. For all its missteps and bad design, WoW has been hugely influential in both the design space and cultural space. No objection.
Quake - Quake was a "Doom Clone" back in the day, and while it was a classic FPS it's influence seems much more minor compared to others. Don't really think this deserves to be on the list.
The Sims - We likely trend towards more hardcore gamers, but the Sims was hugely successful with other demographics. Given the number of sequels and expansions for those sequels it's a HUGE franchise, so either it or the Sims 3 deserve to be on here.
Starcraft II - Controversial opinion time: Blizzard are crappy RTS designers and are wildly overrated. NONE, and I mean NONE of their RTS games deserve to be on this list, save POSSIBLY Starcraft due to its influence in the esports area. But Starcraft 2? Don't make me laugh.
Team Fortress 2 - From a cultural perspective and driving early internet memes, I can see how TF2 was influential. It helped codify the ideas for a class based team arena shooter, and also drove early internet video viewing and viral video with the "Meet The..." series. So yeah, probably does deserve a shout out.
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So to replace the five I've rejected and not offered a replacement for (Witcher 3, Half-Life 2, Portal 2, Fallout: New Vegas, and Quake) I would propose the following:
TIE Fighter or Freespace 2 - Both of these vie for the title of "greatest space flight sim of all time". Both have good stories, action packed combat and controls. Freespace 2, being a later game, has better graphics, but one can make a strong case for either of these.
SimCity or SimCity 2000 - While The Sims is on the list, the entire simulation genre and its massive popularity goes back to these two games. SimCity has the advantage of being first and older, but SimCity 2000 was really the major codifier of what we see as the Simulation game. The fact neither of these was on the original list is absolutely criminal.
Homeworld - You want to list one of the greatest RTS of all time, this one takes all the supposed storytelling grandeur of a Blizzard game and does more in the first three missions than they do over entire campaigns. All while introducing real 3d controls into the mix along with some of the best music (both public domain and composed for the game) to give the game an ambience the like of which nothing else comes close to.
MechWarrior 2 or MechWarrior 2: Mercenaries - The Mech Piloting genre was and is still huge, and these are the two classics that really solidified the genre. While I personally think that the best of the 90s Mech Piloting games was Starsiege, which explored storytelling in computer games as their own thing better than most any other game before or since, as it leveraged things you can only do with computer games to tell the story, IE, it literally had what amounted to an in universe twitter feed that updated with new comments after every mission... in a game published 7 years before Twitter was launched. MechWarrior 2 is probably the game that defined the genre more than any other.
Command and Conquer or Command and Conquer: Red Alert - These games I think defined the RTS genre much more than did Blizzard's offerings. Further, they had a unique flair to them with their FMV cutscenes that just, well, nothing quite feels the same as classic Command and Conquer games. Further, those FMVs made for great viral videos that made their impact bigger than just the games themselves, and the hammy clearly having a fun time with it cheese from the various actors game the games a sense of fun that nothing else quite managed to come close to in the genre.