"Taking a fall" and being whipped around violently by a small girl are two different things. This is a professional wrestling maneuver called a "head scissors takedown." This cannot be performed with out assistance. The attacker is scooped up or assisted by the victim. The attacker wraps the front of his thighs around a standing opponent's head, belly-to-belly with the attacker's toes pointed towards the air. The attacker then whips the opponent around into a "forced" somersault. Here's an example.

Second, this is was not performed to demonstrate taking a fall, but rather to demonstrate a flying submission technique. Here is an example of a flying armbar.

Typically, you don't see maneuvers such as the one depicted in OP's original link as clean or as fluid, because it is so spontaneous it results in something rather messy and painful looking. You definitely don't see someone in martial arts "taking a fall" this violent or in a position where he lands not in the dominant position afterward. If this were the case that he was taking a fall, this would be a very poor demonstration.