Unless I missed something that play is the pinion/ring gear and pretty much normal. If you question The U joints shake the DS back and forth. The caps will stay put, or should and the cross section will move in the caps.
As GATORB8 responded above; do you have any symptoms that you are concerned with ?
While inspecting the front driveshaft pinion end U joint; do you see any rust particles where the trunion goes into the U joint cup ?
From what I can see in the video; the play in the front pinion appears to be normal unless you are getting vibrations when you are driving.