Let's call it SG's or Story games in which the game is driven by narration and the player is just expected to perform task after task to advance the story.  Kinda like Phoenix Wright or Hotel Dusk.

Is that a sequel to the paint drying game?

Woe, ok, that might catch on

You mean, like, ADVENTURE genre?...

Fahrenheit

Hotel Dusk actually advertised itself as an "interactive novel". Kind of wish it was only that because even though I really enjoyed the characters and stories, but the terrible gameplay was just killing me. As long as they're called "games", people will be unlikely to take the game part out. It's a shame really. There defintely seems to be a market for interactive movies as opposed to games with heavy storylines. Kind of like a choose your own adventure book in video form.