Nice game. At first I thought it was going to be a fez like game but no the rotation purpose is to let you see the laser pattern :)
The difficulty ramps up a bit too fast, and the level design is a bit frustrating : in level 3 for instance there is a lot of waiting, and once you know the solution it is tedious to do it, because you only get one second to move because only one cube blocks the laser.
Also I didn't really see a connection with the theme.
Overall the idea is nice, the level design might need to be polished :)