I still can't tell if you're saying that the shooters were kicking up in the air and jackknifing their bodies repeatedly WHILE shooting (as the shooter in the video does), or if the kicking around was done while getting into position to shoot. The former is what I'm talking about. The latter is not.
You keep talking about shooting from "a position" but the shooter in the video doesn't shoot from "a position". He's constantly jackknifing his body and kicking his legs WHILE shooting. His position is constantly and violently changing while he's shooting, and not in a way that would be considered controlled movement.
From any stable position, using both hands on the gun is clearly best. Even from an unstable position, if there's no way to make it stable, a two hand grip is still best. So shooting while standing still, two hands is better than one. Similarly, shooting while running (to simulate the same kind of violent movement in the video) shooting with two hands is better than one. BUT, shooting while standing still with one hand is going to be better than shooting while running using two hands because the tremendously improved stability from eliminating the violent movement of running is going to more than compensate for the relatively small loss of stability caused by taking one hand off the gun.
What I'm saying is that when shooting from an extremely unstable shooting position (resulting in violent uncontrolled movement as seen in the video during the actual firing of shots), that stabilizing the position (making the body stationary--eliminating the violent uncontrolled movement) with one hand and shooting with the other should give much better results than keeping both hands on the gun and trying to somehow compensate for the violent uncontrolled movement caused by the unstable shooting position seen in the video.
(Not unstable with two hands vs. unstable with one hand. Not stable with two hands vs stable with one hand. Unstable with two hands vs stable with one hand.)
As far as shooting between one's legs, I think that sounds ok for a static target, maybe even for switching between static targets if the position of the entire body is changed when transitioning to the second target. For training to shoot a target that can be expected to move, with the instinct (and necessity) being to track the target with the gun and psycho-physiological effects like tunnel-vision potentially in play in the scenario for which the training was intended to be used, I would be completely disinclined to practice any method that had me shooting at a target framed by any of my own body parts.