I'm kinda divided on this. I like the games for the story AND I like games for the fun/challenge. But both levels of enjoyment seem to be totally separate for me. The latter is more like a "hobby" kind of game enjoyment, I like to play games for fun/challenge just as I could pratice some sport or have some other hobby. Something to "kill time", something to just enjoy myself. As of experiencing the story, it's different. I could play a game for the story even if the gameplay sucked hard. That's because I like the general storytelling structure games can have. I enjoy games like this just like I'd enjoy a movie or a book. Of course, not every game has a story good enough to be compared to that of a book or movie. Sometimes, storytelling in games are just that for the sake of being there, but they aren't really the focus.
Someone said: "playing only for the story? go read a book or watch a movie". I don't agree with that. There are a few games with storytelling so immersive and complex that they can beat most books or movies. I say that because I READ A LOT and I WATCH A LOT OF MOVIES, but I can't say there are a lot of movies or books I've experienced that I enjoyed as much as Metal Gear Solid, for example. Also, I like to think playing for the story can improve your cultural references if you pick the right games. I'm a amateur writer (already published some short stories in my main language, Portuguese), and I've used some games' atmosphere as inspirational source for some of my literary works. And that was quite successful, because there are not a lot of writers that actually play videogames. As we all know, art inspires art. The more you read/watch/live, the more you can create. Writers are looking for inspirational sources everywhere. They're constantly reading new books, watching new movies etc. I feel like games can be a fresh and unexplored source of inspiration. They obviously don't exclude the other means, but game storytelling shouldn't be ignored when it has that much potential.
P.S.: Just noting most of the posters in "The Escapist" forums are PC Gamers and/or fans of Western games mostly. All I can read is "BioWare" and "Valve". As much as I like BioWare and Valve, I don't think their games are the only ones that should be taken into account when talking about Storytelling in videogames. I don't even think their games have the best stories at all... but that's just personal opinion.