Yes the key is a little loose and definitely worn.
As is the fit between motor shaft and pulley hole.
I'm not sure if this is intentional or It is worn.
The tiny size of screw through the key into the shaft makes me think it wasn't original.
The hole in the end of the shaft is threaded as if to hold fast the key in some unknown arrangement.
For anyone unfamiliar with this machine, the motor is designed to be easily removed ie. you lift off the motor bringing the keyway key with it but not the pulley. There is no access to the bottom side of the pulley so unless the key is fixed it can drop through. All online documentation I have found shows a different set up to mine.
This set up means no side load is incurred on the motor itself.
Cheers Andy