One Tired EVE Pilot doesn't care about game stories. So who does? That's a question I can't really answer. Role-players? Possibly. Hardcore fans? Maybe. The gamer looking to get lost in a fantasy world? Another possibility.
It's not that people don't care about the story, but they just don't care for poorly implemented story telling devices. I read 1,000+ page books every couple of weeks, but you won't catch me in-game reading chat boxes. I play games to have a living story where a battle is not narrated... it is won or lost in my actions.
Cut scenes in general are poor story telling devices simply because most game developers aren't cinematographers. There is a couple games like Warcraft 3 and Final Fantasies 7-10 that have used great cut scenes to help tell a story, but cut scenes alone do not make a story go. The game play needs to help tell the story as well and that's something I've yet to see done well.
Art is another big area. If a sewer is dark, damp, and stinks like yesterday's garbage... then visual clues like buzzing flies, visual fog, and proper lighting is required. Imitating smell without smell is hard, but artists are smart and I think it can be done without a 100 word text box describing the stench.
The avatar and animations are also important. The way an avatar runs or moves can tell a lot about the history of the character. I would rather see a Goblin Pirate limp across the ship deck than read a text box tell me that he lost it ten years ago in a battle. Resident Evil had your character slump over and stumble as you became injured and it replaced the health meter quite well.
Our minds make the words to the story we see on screen. Pictures are worth a thousand words and a proper game using the proper story telling mechanisms is worth a million.