The two are not fighting (so ignore the title) but the instructor is feeding & testing.
Yes your correct, they have given a little info of their method of training on the website -
Instead, training consists of working to stay protected and aggressively directed while the teacher or another student throws strikes. When we take a turn doing the striking, we get minimal instruction from the Professor, though the receiving student will often slip in a counterstrike if they feel that the feeding student is leaving himself flagrantly open. The real work is the blocking, and the goal is not just to deflect the blows but to learn to parry, pivot and advance toward a strategically superior position. The functional payoff of this method is that it ingrains the instinct to fluidly block an attacker's blows while moving to a position from which – momentarily – you are able to strike without receiving a counterstrike.
we are literally "fencing" ourselves off from the attack. The game consists in trying to get past the opponent's "fence" while keeping them outside your own. These concepts of "inside" and "outside" are really the key to Professor Avril's method.
With this in mind I can see the usefulness of the practice and like Steve pointed out, people are actually killing with these weapons so you would imagine they have some idea of what works and what doesn't. Learning to keep safe and not getting chopped up into little bits being the primary goal then the obvious place to start is blocking and footwork which is what they are doing. Perhaps the nastier stuff comes later and I guess you don't need to be a martial arts genius to figure out how to land a lethal blow with a machete. Often the more simple a method is, the more functional and effective it will be in reality.