What happened here was that we all saw what happens when you have a tug of war on deep wet grass. Tug of wars are all about traction, especially on deep wet grass. Traction starts at the tire to ground interface - the Jeep had the advantage there big time because of it's 'knobbly' tires.
They also didn't use the optimal TR2 settings (there is a Grass/Gravel/Snow mode...not used - this mode locks the rear diff and reduces slip on the center diff; also not clear whether he disabled ESC, which is one button push, seems to indicate he didn't), and it's not clear whether this D240 had Configurable Terrain Response, which allows the driver to control differential locking behavior - in any case, if it was on the vehicle it wasn't used, but it may not have mattered because
the trick in tug of wars is to get the other guy to lose traction first, and the Defender was on ATs vs. the Jeep's MTs.
Locking diffs also help a lot - and a fully locked G-Wagen with a huge torque advantage can make up for poor tires, but only if he gets the jump on the Jeep, and he may have rolled on a little early - the takeoff was skipped if you look closely at the video - we never see the moment when the Jeep loses traction.