The seven games I've played (by far) the most of in the last decade are, in no particular order:
Chess
Starcraft
WoW
Natural Selection
Team Fortress Classic
Unreal Tournament 2k3
Go
No other game comes even remotely close to the number of hours I have /played with these seven, and the only one of the bunch that even attempts to have a story is WoW, but it clearly isnt't he driving force behind the game and I know nothing about it.
So, no. Story is largely a single player thing (RPGs, for example) and I rarely play single player games.
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