Hmm.
I don't want to go too far in explaining things because anyway protein formation is not my forte, but all I mean is that it is irrational to treat amino acids as, say, cards in a pack. When you shuffle the cards, you end up with some random order, and -- assuming it's a fair deck and a fair shuffle -- then there is no reason to expect one shuffled deck to be more likely than another. Therefore all outcomes -- all orders of the cards -- are, to all intents and purposes, equally likely.
Compare this with proteins. If you assume that the amino acids are cards, and can be arranged ("shuffled") in any order, then you end up with a phenomenally large number of possible proteins, possible arrangements, etc etc. The argument of the video rests on this premise, ie that there's no reason to prefer one arrangement to another.
I claim that this premise is false. The reason is quite simple, in one sense: the amino acids are not the same as the cards, because they actually *do* interact with each other. They care about each other's chemical properties. The arrangements that form, or twist into weird shapes, will have different properties, such as the amount of stored energy.
It doesn't matter too much about the details: the only point is that you can't treat amino acids as independent of each other when they form proteins. As a result, the "card model" that's used in the video is simply inadequate.
Does this make sense?