What a daft thing to say. You're essentially counting out pretty much every platformer (which don't have much stories beyond save the princess, etc.), rhythm games, the vast majority of Nintendo games and more.If the game doesn't have a story, it's really not worth playing unless it's a puzzle or simulation game.
Hence why so many games are shallow and uninteresting these days. If it doesn't have a story, what's the point in making an action game of any sort?
Chess doesn't have a story, what's the point of boxing millions of chess boards a year?
In the end, regardless of personal preference, people play games because they want to _play_ them. Story isn't playing. There's maybe 5 NES games with anything even remotely resembling a story: we all played the crap out of every one of them in the 80's. And we all have stories of "the time we discovered whatever" or "the secret (but bullcrap) way to do this thing!" or "this fun time I had with my buddies while playing."
That's what makes games fun. Professional sports (the ultimate game, perhaps) has a total lack of "story" as opposed to an incredible amount of natural drama that occurs when they all play a game with absolutely zero inherent story. The story is the story the players make as they strive to achieve victory against each other.
That's what games are about. Not canned dialogue-heavy "story" that you either click A through hoping it ends soon or stare at going "oooooooooh shiny!" until the next numbered sequel comes out. That's why there are so many shallow/uninteresting games these days. It's because they give you the same story that was boring 100 games ago with new characters, hype you up into believing it will be new, and then taking your 60 bucks.
Minecraft: zero story, 6 million players, immense popularity and acclaim. Tetris: zero story, millions of players, beloved game.
Just imagine Tetris having a cutscene explaining to you that you have to put the blocks into position to prevent an evil madman from using a mechanical T-Rex from launching nuclear missiles. Pretty shallow and basically uninteresting, right?
Yeah, story in games is dangerous and rarely used well.
The Princess is in another castle: all the story SMB ever needed, because you made the rest up on your own and with your friends.
Interactive movies aren't games.