You have a pause in there where the tiles take a moment. Please let us use that pause to rotate a second time before the tiles fall so we can also get the pieces to move across the board rather than just slide parallel.
Very fun take on the old 2048 concept, but I'd better stop playing now otherwise I'll be on it all morning!
My only suggestion is to add control by cursor keys in addition to mouse.
I have no idea what it would look like, but it'd open the pool for strat on solving the puzzles I think. May need to play around a bit with the shapes and materials to make it more interesting though.