This was fun!
The unmovable blocks should be colored much more differently than the movable ones. Maybe make them black vs white instead of 2 different grays?
If you allowed mousewheel scroll to move the selected block, this could be a 1 hand game.
I'd like some sounds added to make the game more lively. At least an exciting sound for when the player gets a block to the exit. Maybe a sound that plays while a block is sliding too.
Maybe replace that gray background with a picture of clouds or stars to look more interesting.