Pre '99 they have torque biasing LSDs, with which one could use brake throttle modulation when one wheel was in the air to brake it and send power to the other side. The '99+ models used electronic traction control, where if you just hold constant RPM (instead of rocking like in the video) the computer will eventually get power to the wheel with traction.
Either way, driver in the video is and idiot, it is a case of driver failure, not equipment failure. If he knew how to drive that Hummer, he could get off that easily.
The AMG Hummers are some of the most impressive stock off road machines I've ever seen, with their heavy weight and wide wheelbase they don't loose traction often, and when they do there are ways to get power to the other wheels (see above). Their only major drawbacks is their width and turn radius keeps them off many trails. Oh and of course the price $$$
P.S. I'm not military, just a fan of the AMG product, the military ones may be different then the civilian ones.