I did like you point about if you go outside console gaming that what you would claim as the most influence game of all time a PC game. It may be better to say the Most Influential Console Game and the Most Influential PC/Other Game.
In my assessment of the former, I am inclined to say Halo 2 is contender for console, because the Online play, and the Campaign with a twist in who you play as protagonist is pretty epic.
I think PC gaming led to like Minecraft and ultimately a lot of independent games, mobile games, in addition to the social media network stuff.
I just think it's crazy the influence MMORPGs in general have had. It kind of changed a lot of people's lives with online interaction and led to sort of gaming as a lifestyle as opposed to just a hobby.
But yeah consoles and handhelds did their own thing the whole time, and in that space Halo was pretty momentous.
In fact if I were to focus on console games I'd say the most influential have been NES Super Mario 1, then probably Castlevania SOTN.
With Super Mario 1 it basically established the core trajectory/formula in like all console games, which is like, 1-1, intro tutorial level, ramping difficulty, secrets, bonuses, like so many things are just in like every single console game.
I would actually say also the most influential games are Pac Man, Space Invaders, and Street Fighter 2, but those ended up being more flashes in the pan I think. They're really epic and important but I don't think people were in a hurry to build off Space Invaders and Pac Man so much as use them as springboards to make their own kind of interactive game. Street Fighter 2 for fighting games was really big but then fighting games became niche.
I think after SOTN would be Ocarina of Time, as the primordial 3D action game.
It's kinda lame because I like Ocarina the best, but I think people got fixated on the combat possibilities and so they made strictly combat oriented 3D games like Devil May Cry and later the souls series whereas the original Ocarina had more of an immersive exploratory/unique feel to it.