I like how you implemented the limitation! Sharing one 'controller' whilst each player has a different objective is a cool idea!
I did find it a little hard to control - the spinning arrows made it a bit uncontrollable at times, especially with another player (admittedly, myself again) trying to work against me. Maybe slowing down the arrow or giving the players WASD and the arrow keys to work with would help? I also noticed that there was a cooldown, but I wasn't entirely sure when this cooldown was over.
I do still think this is a neat game and your implementation of the limitation is definitely something that could be expanded upon!