The looseness you show in the video is normal, for AC pumps it is necessary for the magnet to get a start spinning before it has the resistance of the impeller, propeller or needlewheel, the only exception is with rare earth impeller magnet or a motor with capacitor to give a "boost" to the start up.
The needlewheel is out of balance and should be replaced, either the hole in the middle is not round or it is off center. I would write to Tunze in Germany, info at tunze dot com.