pretty cool concept for a puzzle game, visuals and game backstory are cool too. I have a single piece of criticism:
the controls make sense, but they are never explained, so I was trying to figure out how to play the game for a full minute . Some visual indication on how to play the game, say a cursor sprite that's shown moving and indicates dragging the column if the player has yet to make a movement after 15 seconds would make a ton of sense.
Also, to play in the puzzle aspect, you could give an objective for each level to complete in less than x turns, or even give an award or some kind of completion thingy if the level is completed in the least amount of turns possible, just an idea.
Well done on submitting for the Game jam!