HOW is the vehicle jacked-up? Right side tires off the pavement, BOTH left side tires still on the ground?
You do not have a locking, or limited-slip differential in front. Power flows unevenly, so that if one wheel is stationary, the other spins twice as fast. If one wheel is spinning at 1/2 speed, the other is spinning at 1 1/2 speed.
Yeah, you may have a gearing mis-match. I'm not thrilled with your video showing how you determined that, though. "The shop" supplied this differential. You need to jack them up about the potential gearing mis-match.
Dry pavement, 4WD. Does the vehicle bind-up, act like it has no power?