Beta males have no one to blame but themselves for their lot, but I don’t follow the logic.
(I should have noted that while I brought up the word myself, I don’t really like compartmentalizing men in such terms – but I’ll use the adjectives alpha/beta simply for lack of better terminology.)
Without agreeing completely with their stance (I should have noted that before as well), let’s just say that it appears to be a resounding claim by “game” theorists that women are hypergamous. This idea is also echoed by some evolutionary theorists that say men are polygamous, while women are hypergamous (which seems to have replaced the old theory that said men are polygynous, while women were monogamous). The main concept/complaint (from what I have gathered in reading their concerns) is that women today, being able to make their own money and therefore becoming less dependent upon men for survival, have been “freed” from the social pressure of marrying young and are acting upon their supposed hypergamous tendencies by delaying marriage to a suitable “beta” male so as to continue to seek out a more wealthy/dominant “alpha” for either marriage and/or mere entertainment/enjoyment. Part of that theory is that as a result, women who fail to obtain the alphas they want end up “settling” for a beta as they reach the later part of their fertility cycles.
I suppose the logic is that if polygamy were legal, and there were a plethora of women willing to enter into such arrangements, all of the young beautiful women would be snatched up by alphas, leaving a disproportionate number of men womanless and childless. I think this outcome would possibly become inevitable if the middle class were wiped out and the vast majority of the population was so poor as to be on the verge of starvation. As things are currently, legal polygamy probably wouldn’t have much of an impact on society, so maybe I’m thinking too far ahead with regards to economic disparities.
Alpha males, at least in the common parlance, have zero interest in actually making a lifelong commitment to women. Or they do make a lifelong commitment but not one that involves property. There’s a reason that guys like George Clooney and Derek Jeter don’t get married.
I do agree that some “alphas” would always behave as butterflies, flitting from one woman to another. But I also wonder if there is a separate class of alphas – those like Donald Trump, Larry King, Rush Limbaugh, Henry VIII??

etc. – who would take advantage of the legality of polygamy. Maybe it would have something to do with legacy and inheritance of businesses. (Is that what you mean by property?)
I’m not supporting their decisions, by the way, just noting that guys who choose to live that secular lifestyle are not going to make the “error” of marrying one woman, let alone multiple women.
You do have a good point here as well, as far as noting how the current layout is in this country. As it stands, I also wonder if this has something to do with current divorce laws and post-divorce settlements. It’s all speculation, with things being as they are now, but I wonder if there were no such thing as no-fault divorce and alimony, and the economy took such a drastic downward spiral as to leave most men (and women) barely capable of supporting themselves, would the George Clooneys, et al., then be more inclined toward marriage with multiple wives?