It seems they do 5 vs. 5 matches and that sort of thing. A team loses when all of it's fighters are defeated, like team deathmatch. To defeat someone it looks like you have to push him to the ground or knock him out, which results in the same thing of course.
There could also be some sort of TKO but I don't know for sure.
I wouldn't say it's just an angry mob bashing at each other. If you watch some of the fights you can actually see different techniques they use to defeat their opponents. I'm pretty sure they train a lot for these fights, but not any Talhoffer stuff, because reenactment of medieval combat is not their goal obviously... This looks more like team wrestling with the addition of blunt weapons and armors.
