I'm still not the guy to talk, because I'm not really invested in the argument and don't play games, but I'm having trouble imagining a story-telling game that doesn't require non-player cut scenes to, you know, tell the story.
Unless it's a choose-your-own-adventure thing entirely, like a tabletop RPG with a GM, how can you "play" through a story? Play is inventive, story is didactic. They don't seem to gel. From what I understand (probably wrong), even war story games are basically "[thing happens in non-playing mode] shoot for a while [thing happens in non-playing mode] shoot for a while," etc.. That doesn't make this game a "story game" and Doom "not a story game," it just makes it Doom where they've cut in a movie between levels. Or more specifically, it makes Doom a game where they didn't do that. Right?
Even Portal, which again, also gets the "from what I understand" label, is basically a cool game mechanic that you fuck with on harder and harder levels as they drip a story on you in details peripherally. The details are really fun, and I love that song, but assuming I'm right about that (whether or not I am, but for the conversation to ensue), can you really call that a "story game?" Some large fraction of what people like about Portal, as Doc said, is just fucking with portals. GLADoS and all that makes for a cool backdrop, but it's a setting. Right? It's a setting that explains why you have a portal gun.
= story?
The question in the beginning of the thread boils down to how you define art. The question for me now is, how you define story.
It seems like you can have a story, and you can have a game, but you can't have both. If it's a game where the story is locked down and gonna happen the way it's gonna happen - you know, like a story - that means whatever pre-programmed activity you're doing to get to the next plot point isn't much of a game. It's just an activity. Meanwhile, if it's a game that you're playing, you should have significant - if not total - control of the outcome, and bring strategy and invention to the table to eventually win. Otherwise it's tic-tac-toe. The base requirements of a story, and the base requirements of a game, seem to sort of exclude each other.