According to the description, this is part of their black belt test. I like this video because the moves are executed fast. In practice moves are normally practiced slowly and controlled, so many people doubt the effectiveness of aikido techniques in a real situation where people would be moving much faster, and at all sorts of angles.
Where there is truth in this, a person who is new to aikido would probably not be able to execute these techniques against a knife, however for the experienced akidoka who has been exposed to the same moves over and over again, defending against it should come as naturally as covering your face at the last second when you think someone or something is going to hit you.
Note that I said defending, which means the aikidoka would wait for the assailant to attack before executing their counter. Instead of trying to grab the knife, the aikidoka would wait until the attacker made the first move, and the theory behind their training is that most moves are essentially the same during attack. These moves consist of stabbing and slashing, which is what aikidoka train to defend against in the first place.
However, does being able to execute these techniques easily and flawlessly in the dojo mean you could do it in real life in a real situation? Perhaps, perhaps not. In practice, you are relaxed and know you wont get hurt. You can tap out, cry, and basically take your time standing there while thinking of what to do. In a real situation, where someone is trying to stab you, you may only get one chance, and so the aikidoka has something else they need to train for, which is, learning to deal with the pressure.
So how would one simulate this pressure in a training situation? The answer i suppose is grading, especially black belt training. Here, the pressure to perform is high, as failing to execute a technique could mean failure and waiting another year or more depending on your level before you can grade again, and that's just one source of pressure. During grading, your peers are watching, your master is watching, other masters are watching, the girl or guy who you have a crush on might be watching. Your heart is racing and you feel like you're gonna throw up because of the pressure and the instructor shouts "Hajime!", and suddenly, its show time.
This pressure can get so high in fact that you feel that if you do not perform you could die, and i think its when an aikidoka reaches that point and realizes they can execute a technique, only then would they stand a chance in a real badass knife situation, unless your attacker is an amatuer, slow, or you get lucky.