Well, the video wasn't the greatest quality, as I couldn't see into the diff extremely well.
If the rear tires are on the ground, I would check the cross pin hole on the locker, they maybe have become elongated, and therefore the carrier will start to move, and the locker should too, but since the hole is oblong, the crosspin can travel in it a short distance, then bang into the side of the hole, creating the banging noise you are hearing, and providing the slop you are seeing. (The carrier spins a short distance before it puts load on the axle shafts)
If those tires are jacked up, and the transmission is in park, I might check out your transfer case.
Edit: I would definitely check the cross pin hole in the locker.