Realistically, there's gonna be one question per game doodle and one game doodle every other week or so. So it's safe to assume we could just have them all under a collective google-doodles, sort of like a set of minigames. The tag wiki should probably include a note that you best link to / give a date for the doodle in question.
We also have the precedent (for google-doodles) set by the Zerg Rush Doodle (64300)Zerg Rush Doodle (64300), we could just consolidate them all. (And probably also remove the uniquely identifying google-zerg-rush there.)