The wobble in the clutch hub in the video is normal.
I believe the problem with the OP`s bike is that the pulley nut has come loose.
Another way to immobilize the clutch hub in order to loosen the clutch hub nut (also the pulley nut):
Remove the transmission top cover and shift drum.
Move the shift forks around until the transmission is in two gears at the same time, the transmission shafts will now be immobilized.
I believe the problem with the OP`s bike is that the pulley nut has come loose.
Another way to immobilize the clutch hub in order to loosen the clutch hub nut (also the pulley nut):
Remove the transmission top cover and shift drum.
Move the shift forks around until the transmission is in two gears at the same time, the transmission shafts will now be immobilized.