Though this is an older app, check out Fragmental 3D for inspiration. It's a 3D version of Tetris, so it fits right in with your idea.
The actual gestures you decide to use to manipulate the shapes are up to you. I think I would use a swipe as you mentioned for moving it side to side, a grab and twist motion to rotate it, and a swipe downwards to make the piece fall—but those are just off the top of my head and totally up to you. I would design it and then play with several versions until you come up with your ideal motions to move things.