The PLA practice combat Sanshou as mentioned by one of the posters earlier. It combines striking, take-downs and a little bit of grappling. No fancy moves whatsoever compared to those Kungfu movies. It's more comparable to Mixed Martial Arts style fighting.
Hand to hand combat training is not only great for physical training, but can enhance a soldier's mental toughness and confidence in his abilities. I feel much better now going to night clubs than before I took up kickboxing and Jujitsu few years ago. We do have a hand to hand combat course in the Canadian army, but I never attended it and learned the arts on my own time.
Do they teach any wrestling or grappling in training? It seems like they stop whenever someone hits the ground.
They too teach a mixture of martial arts styles and techniques that "work" ie: the headbutt shown in one of the moves.
That video was of a demonstration team, obviously they put on the "flashiest" moves for the crowd, though I can tell you from my unarmed combat course years ago, that we do indeed get "down and dirty" when training for this...
Grappling is very much a part of the training. As is biting, gouging, headbutting, punching, kicking etc.