Well there's your problem right there. [LOL]
Printable View
there are two sides to that front diff, is the driveshaft still installed? what is the t case doing? have you removed the carrier? are you sure there is nothing broken on the pinion gear?
Ok. Finally watched the video.
Your front wheels are going to want to spin/rotate a little when you are parked. If you turn to the right the right side will rotate back, and the left will rotate forward. Not much, but maybe a degree on each wheel perhaps. This is going to cause the spider gears to rotate a little bit. What I think I am seeing (and yes I realize this is now probably way to late to help OP's friend) is the joints at the wheels binding up. At least one of them. I would bet if you put the front end back up and spun the wheels with the steering all the way over you would have a tough time with it.
Also your front end is locked. Unlock it and that might take care of the issue.