About the only example that comes to mind is last year's Attack on Titan: Wings of Freedom, because it's superbly fun on the gameplay front and I'd recommend it for that alone, but it's also an adaptation of a story I already know, and the cutscenes are just 3D-rendered scenes from the anime that don't matter.

Aside from that, I honestly can't think of many. I'm a big proponent of gaming as a storytelling medium, and I'll give any story a shot, even generally throwaway ones like 80% of fighting games. I don't recall ever actively skipping cutscenes for any game except when replaying pure gameplay-focused ones.