There is a case to be made that some games are so incredibly influential, that they carried a year on their own. Think the year Tetris was released or the year Minecraft was released.

That being said, we have 2004, which had WoW and GTA San Andreas, both of which are up there for the most influential games of all time. Pair that with a few other gems like KOTOR II, and I think that year should take the cake.