Atoms and molecules attract each other and produce an almost infinite variety of chemical substances. It's part of the chaos that exists in the universe. When things combine because they have a natural affinity to do so, they simply do so. And they do this whether the universe is chaotic or not. There is so much of this natural affinity creating so many chemical substances among the existing chaos, that it seems random, but it's not really random, because of the natural affinity that exists. It happens because it's going to happen.
When simple things combine into new more complex things that go on to combine and make even more complex things, the results can be unpredictable, and that makes it seem like a pattern exists in the chaos. Of course, none of this is directed, predicted, or predetermined. If that's the definition of "random" then I'm OK with that.
I suppose, I'm missing the point of the short video, but it seems like that speaker was suggesting that scientists might be looking for a pattern to randomness, which would be absurd. Randomness literally means "without a pattern." This is not to say that life is inevitable any more or less than carbon dioxide is inevitable. It's just one of the trillions of outcomes of the affinities of complex combinations of elements.
We act as if we are surprised because life exists, but that surprise is just an emotion that arises from our confusion. Things happen whether we are surprised, disturbed, elated, or surprised again. No reason to be surprised, really.