This vid is pretty good at what the participants state it is supposed to achieve. We can see that the tanto wielder is giving his hand to his partner and then the exercise starts, this is not tanto dori as they stated.
This exercise is done by us actually as part of our tanto randori training for shiai. If I may just make some observations based on the vid:
The knife wielder has many opportunities to throw the empty handed partner via sokumen, irimi nage, shomen ate, ushiro ate and a host of other throws if more hip power and rotational force were used to end the face to face stalemate that happened once both hands became occupied with holding the knife hand and the other arm of the attacker. This actually shows how the Aikido techniques that are based on a wrist grab are designed to work. When one is resisting and trying to control the knife, the grab on the knife hand is very strong, this force can be used to do a host of throws and other waza just as they are practiced against wrist grabs in kata.
Like I said, not a bad vid to illustrate its stated goals. It looks quiote familiar to me.
As regards dealing with a trained knife wielder it may be best not to be unarmed if one can help it. However, attacks rarely catch us at our best so serious tanto training does have its place regardless of whether one will get cut. That is par for the course imho the key is to understand the dynamics and include "getting cut" as part of your training approach so it is dealt with.