Sigh, somehow I knew that I'd see Halo and WoW up here, and suddenly I feel kinda old. To truly change history, you need to start at the root, and that's why I'd choose one of these:
Everquest/Ragnarok Online both were among the first MMO's to make a big impact in MMO history. Everquest for Western audiences, Ragnarok Online for Eastern, (and PSO for console, but I <3 PSO so shh). Both had elements that would later infect the market (for Everquest it was buying/selling things on "Ebay" for real money, Ragnarok it was endless grinding leading to botting), and cause a strange rift in the market that WoW resolved (and subsequently why there's a ridiculous amount of players in the US and Asia). Even though I've sampled both of them, I'd still axe EQ over RO.
As for shooters: even if you hate shooters, you can't hate Goldeneye for what it was. It was a supremely crafted shooter with a good story and awesome multiplayer on a CONSOLE. If I could change history, I would have had Rare become the next hot company (and have Bungie go further down the path with more games like Oni). If I couldn't, then I'd eliminate UT2k3. UT is a classic that belongs in the archives with QIII,etc. but everything devolved from there (there were a few nice perks in 2k4, but it just felt tired). CS and Halo are actually decent games when viewed on their own.
As for RPGs: If I could change video game history, I would have modified the N64/stopped FF from going over from Nintendo to Sony. I seriously believe that FFVII's acclaim was the product of Sony's hype bandwagon + 3D + having an epic and decent game (I'm not saying that it wasn't deserving of praise, just not so much). If I couldn't...then I'd probably have to go with FO:Brotherhood of Steel. It was so...meh. Or maybe FFXI?