With cassettes it really depends on the wheels and hub design, you can get a little wobble even with the proper spacers but you shouldn't get much.
Freewheels (where the ratchet mechanism is part of the sprockets) have a lot more wobble inherent in the system as a consequence of the bearing position. It looks as thought that might be a freewheel rather than a cassette - you can usually tell by looking at the hub, there is often a slight bulge on cassette hubs on the right hand for side looking from the rear (see
here for more info - but note this doesn't apply if it's a through axle rather than a traditional QR).
If it is a freewheel then the level of wobble might be within whats expected, but you'll need to post the video as
@ColinJ says.