It would be a movie where you control the pace of the plot
Sounds interesting. Perhaps actually having the game there, but also being able to bring up a game menu, and in it have the option "Skip to next Plot Point." then the player can stop playing that section, and they will immediately move on to the next section, with the story continuing. Then give the player 2 options when the story telling is done, "Back to game mode" or "Skip to the next Plot Point".
And finally, you could have an option at the start of the game to just do "Story Mode (No Game Play)", where it skips all game play.
Yeah, I think a game made only to tell a story isn't really a game anymore.
But I think Prinz makes complete sense. If all the options are taken away from the player, and they don't do anything except click continue, then its just a story, not a game. The player needs something to do, something to play, or its not a game.