You don't want that box loose on the blower shaft, it will flop back and forth on the key and wallow out the key way, destroying the shaft.
Usually there are 1 or 2 set screws that both hold the key in and lock the gear box sleeve to the blower shaft. But the alignment has to be good or it will move around anyway. (if this was a spline that transfered the load you'd be OK).
Dan