Transmission, drive shaft and differential question

Here is link for video:
[URL]https://karjalandatahuoltooy-m...NHut7tSM-fvNUBTEkxfiZbhGyLhidGGzeFIQ?e=czID2i[/URL]

Sorry for bad quality, hope you can see free play between gears.

That looks pretty normal to me.

Try getting the rear off the ground and run the car at speeds where the vibration got bad.

Tires can vibrate at speed (especially combined with a bad shock absorber) and so can a bent driveshaft.