Thirding Telltale games, though I have more tolerance for the basic gameplay and think the "meaningless" choices get far too much flak -- I can't often get immersed in the master-class storytelling and characters if my hands aren't on the controller. Most environmental narrative games / "walking simulators" and plot-focused indie RPGs like The Crooked Man or To The Moon, as well.

Really, the pick that always jumps to mind for this subject is Asura's Wrath. The story and fight cutscenes are some of the most grandiose, outlandishly scaled, and yet strangely moving stuff I've ever seen, and the world and characters are pretty interesting and unique. All the same, the best parts of it are barely interactive beyond admittedly satisfying button prompts, and the active combat sequences are repetitive, wafer-thin, and free of challenge. It's one of few games I can think of that provides exactly the same experience whether you're watching a good playthrough on YouTube or playing it yourself.