As a professional video game developer, right off I can tell you you're making fundamental mistake: you're thinking about the story and not the actual play. "What's the interaction? What do you do? What are the objectives, win and lose conditions?" Those are what you need for a game. The story is merely the setting. You need the gameplay to be compelling. The story and setting is frosting. You need the cake.
I'm kind of there too; senior in a four year game design program. Sorry to have not said it; but it's sort of assumed here. UDK-based class; but game as dialogue driven with the shooter core. And yes, story-focused in this case; it's kind of a reaction of the Stanley Parable which is almost all narrative. Also, I'd personally say the importance of story varies from game to game; the core game mechanics of Amnesia for example would be droll without a story; but inversely Sonic games don't need a story at all. Story/writing is at the core of this though.