OMG, that pinion bearing is toast! It was tightened way too much!
It should spin over with just a simple twist of the wrist. Normally you can't tell on a video how much pressure someone is applying, but I can see that it is taking way more effort to turn the pinion yoke. And that noise, should be just a whisper whir as it turns, and it should turn smooth, not feel like it has lumps in the rotation.
I accidentally over tightened a pinion nut on my own vehicle when I did a pinion seal. On my drive home the pinion bearing seized and the rear wheels locked up and I skidded through an intersection. That was my first pinion seal job and I'm glad it was on my own car. It's not very complicated to replace a pinion seal, BUT, you CANNOT make the one mistake of over tightening the nut. Their are simple steps you can take to prevent this from happening, they didn't follow them.
And, they may say it's just coincidence that this happened, no way! If the bearing failed it would normally be very loose, your pinion is very tight.
Bad job, go back and have a senior guy do it or better yet go to a driveline shop that specializes in diff service.