A poster on Sherdog explains the move a little bit a few posts down.
It's actually 2 techniques that flow well together... he starts from control of the upperbody from double underhooks from butterfly guard, pushing off and shifting opponents weight and then using the momentum to sit up (in this case they actually stood all the way up), and then before joe could pummel and get and over-under, since nathan already had hip control with his grip (see how he shifts his double underhook from up high when in the butterfly to down low when they're standing), applies pressure with his head up top, pulls in the lower back with his hands, trips and gets the takedown.It seems like Marquardt gets his initial momentum by kicking out with his hooks, driving Doerksen's hips back. That is what gives him the space to stand up (using Jean Jacques Machado's quadraceps killer drill!). It also moves the center of gravity back off of him.
It's a nice move. Since I've been trying to work the butterfly guard more and more, I'm going to try and incorporate it into my game.
Another point. Having one hook in and the other leg around the guy's back/thigh is okay if you're setting up a sweep in the direction of the "overleg." But you don't want to stay there because it is a holding move at best. It is better to put a foot in the hip to break the guy's posture than to "waste" that leg wrapping it around the guy's back/thigh.
Again, if I'm going to sweep in the direction of the overleg, say while kicking out with the underhook leg on the other side, then fine. But I can't just sit there.
I've also got to sit up and get my hips under me. No lying down in the butterfly guard (they don't call it the "sitting up guard" for nothing!)