Some games need story. It depends on what type of game you want to make. If you want to tell a story through your game, you definitely need one.
Not all games are simply about "haha let's have light-hearted fun". You seem to generalize in a way that suggests that no game would need a story. As if no game were ever designed in order to tell a story. Which is an erroneous assumption. It's as if you're trying to limit the definition of games to "gameplay-centric games only", passing off everything else as something completely different, not even a game.
A good example is Shadow of the Colossus. I don't like it mainly because of its gameplay, but rather because of the entire experience. The amazing surroundings just there for you to explore, the atmosphere created by the music, art, design, and subtle story, as well as gameplay. Remove any one of these elements and the game falls, because the experience that the creators are trying to achieve wouldn't be complete. The game doesn't even have much of a story, and you can definitely neglect it, but you wouldn't get the same full-fledged experience. You get my point?
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