Video game are just a different form of media - I read books and comic books, video games can tell different stories, too. Due to their nature, they can tell different stories in different ways than would be able to be told via other media forms, including movies, television. A lot of times, the story isn't really something that would shine as well in a book/comic/TV/movie, which is why they put it in a video game.
Then again, many video games just have excuse plots that don't really matter. A video game doesn't need a plot to be good, it just needs to be fun.
That first paragraph is sort of a misdirection - the real reason why I like playing video games is that I relish the challenge. Whether it's beating someone in head-to-head on even ground, or managing to outsmart a computer that has an edge on you, being able to gun for victory as hard as you can gives a similar thrill as when you're playing sports. Hell, look at WOMBO COMBO - people get just as excited over some video games as they do over sports.
I can think of a few examples. The first time I played Metroid Prime, fighting the Omega Pirate was incredibly hard. To be honest, the guy scared the bejeezus out of me, and he killed me something like 10 times. When I finally beat him, I wanted to get up and high five everybody. Hell, my heart rate was close to 150 bpm, I was so into it.
Or playing early Resident Evil games, with the fixed camera angles, when you walk into a room, you can't see a large part of the room. Sometimes there are zombies in there, sometimes there aren't. You have to bravely take those few steps to get the camera angle to change, in order to see what's in there, and sometimes those few steps send you right into the maw of a zombie. I'm on edge the whole time, and relief floods through me when I enter a new room and hear the "safe room" music start to play.
So that slightly out of breath feeling when I get done playing, that really ain't something I'd get unless the game is super challenging. That's what makes it worth it to me, and what makes me like playing.