I agree with what Kibate said. The pieces should not be sticky. Let the idea go wild, I want to drop a piece at full speed and bounce everything around!
I would recommend you check out Not Tetris 2, which is a version of Tetris with rigidbody physics. It handles line clears by cutting the pieces like you mentioned in your video. I expected a softbody version of Not Tetris 2, but the stickiness of the pieces doesn't help.