How do you know that humans aren't meant for only one other? You have just as much actual proof of this as the alternative. Perhaps if the divorce laws weren't so inherently favourable to one particular side of a marriage (usually the woman due to how the resources are split), divorce wouldn't be the huge factor you see it to be.
In the video, there was no mention of the man seeing any other woman on the side. It was simply the woman seeing other men. I would hazard a guess that if the man did attempt to see other women, his wife would promptly divorce him. Not only this, but due to the fact that he is the one doing most of the work raising the children, can you imagine the impact it would have on them if he began spending his time seeking sex and wining and dining other women besides the mother of his children? The problem with this paradigm is that there is nothing good that can come of this for the kids, and they are the ones who ultimately suffer.
What you are describing with the "marriage where both partners see somebody on the side" is not really a marriage at all. Until you've actually tried this and seen it work and not had to justify all of the misgivings, lack of trust, negative consequences, and communication breakdown that occurs from this, consider me unconvinced that it's a good idea for you, let alone anyone else, especially where children are involved.
The main issue that the video tries to bring up is that equating monogamy with patriarchal oppression is just completely wrong and blatantly misleading. It has about as much to do with feminism as your mom baking a cake for your dad on his birthday or your brother reaching for something on a high shelf for you because he's taller. Trying to make everything about feminism is not only intellectually dishonest but outright damaging to those who lack discernment.