Youtube link fixed.
"unplugging it" from under the truck probably means disconnecting the transfer case's connectors (on the 4.0L engine, not the 4.8L) -- which disables 4wd. But doing a burnout is one way of increasing the likelyhood of transfer case failure because during a burnout, the clutch discs associated with the rear driveshaft is spinning very rapidly (exactly how rapid is calculated by the wheels rotation per minute multiplied by the gear ratio of the axle) while the clutches for the front driveshafts are not spinning at all. These two groups of clutch discs are in contact with each other and the only thing preventing them from burning each other out is the fluid in the transfer case. But as this fluid is heated up, it starts becoming varnish-like and its lubrication properties severely degrades.