@Vaft,
All of it. Let's analyze just a few of the ways.
What, if you boil it down, is the relevance that the facts you present (assuming them all to be true, which is dubious) would have? You say it is not to argue that polyamory is RIGHT, just NATURAL. OK, let's play with that.
So you're saying that it is our nature to have trouble being monogamous....
Wow, really Sherlock? I guess nobody knew that before now, huh? Probably all the literature from time immemorial that explicitly made this very point in every possible way was just playing, and they actually meant that it was totally easy, given our natures, to be monogamous. Man, thank God for modern science to give us these incredible insights.
OK so, sarcasm aside, that's obviously not a new insight, so you must mean something more -- that this somehow legitimizes a non-monogamous lifestyle, or de-legitimizes society's decision to de-legitimize a polygamous one. But here, it simply fails. It's "natural" -- so what? Lots of things are natural that we're very happy to have done away with or outlawed: rape, violence of men against women, violence of men against men, theft, and murder all have deep-seated roots in our natures too, and you can do the same evo-pscyh analysis to explain them. So should we look at those as OK, too?
No? Then what relevance does any of this have?
"This is why people cheat, and why people have ludicrous jealousy when their partners are sexually interested in others, because they assume that their cultural view of relationships is true."
Ah! There it is! Because something opposite may be "natural," my cultural view of a relationship is not "true." BS! If I want somebody to be devoted only to me, then that's what I want, and there's no true or false to it. Is a woman's desire not to be raped also "not true" because you can give an evolutionary psychology explanation for why rape happens? What people assume in relationships is that they want their partner to be monogamous; that their partner, being human, will be tempted to have sex with others; but that they require/desire a level of commitment that will entail those temptations being resisted. That is perfectly true, perfectly valid, and good, and nothing in your analysis (or summarized analysis) even vaguely hints otherwise. You're drawing absurd conclusions.
OK, so it's irrelevant. Is it even valid anyway? No. First of all, what's so special about the hunter-gatherer groups of which the authors speak? Maybe they did live like that (though see below), but what impact does that have on us today? Maybe we're evolving to be less like that. Maybe we have been for a decently long time now. It would seem so. Is that bad? Is it something we should reverse? Maybe the species will survive better if we become more monogamous. Pressure has favored that for the last several millenia, for sure.
Finally, there's the question of whether the book is actually even right in what it describes. There's no reason you should take my word for that, so I'll leave you with the review from the journal "Evolutionary Psychology":
www.epjournal.net/wp-content/uploads/EP09325335.pdf