Yes, story is REALLY important to Pong. I mean won't it be nice to knwo the story behind the beloved blocks in Tetris? Oh Man, that blue one is Hoooot.
I mean, not all genuine of games require a story. Some games REQUIRES a story of some sort to be playable/enjoyable, while the others can work just as well without one, or probably they work better without a story.
Playing an rpg w/o a nicely written story is just boring, so did playing tetris with a minute long storyboard and video between each level.
I mean, does it really matter about the story when you are playing a shoot'em'up? Counterstrike works quite well without any story. AoE, once again, is a good example. Same goes for many fps type.
Oh the other hand, you can't have resident evil without good atmosphare and storye\telling, rpg would be moot without a story, and hack Zelda won't be the same if its just "elfboy in tights slashing things"
Its somewhat like storyline in pr0n really: There are nice ones with good acting and storyline and mood so it is quite ejoyable, but sometimes just plotless mindless action is allright and fun too.