The largest human “pack” size is 37800000

Dunbar's number would suggest otherwise. Human "pack" size is closer to 150. Past that, you really don't recognize or interact with people to consider them peers.

But the rise of "Alpha Male" psychology seems to be paired with the gamification of dating, particularly via for-profit web apps. There's all this meta-psychology blossoming around a simple mathematical problem of too-many-dudes for too-few-women in a setting that rewards aggressiveness.

What we have is a totally artificial environment lauded by bunch of NEET libertarian techbros who are then forced to rationalize why they can't use it to get laid. In some sense, its like that scene from "A Beautiful Mind" except replace John Nash with Andrew Tate, and he's telling everyone at the table to fight to the death over the one blonde girl.

But the heart of the problem isn't simple that humans aren't wolves. It is that you have made of yourself a pack of caged animals and tried to explain the resulting social dysfunction by appealing to naturalism. Even if you were right and there was a chicken-like peaking order rather than a giant dog orgy instilled in the human psyche, you couldn't take advantage of it because you have become locked in a hen house overwhelmingly composed of roosters.

Incidentally, gay dating apps have an entirely different dynamic. There's no "gay alpha male" theory to contend with because they're all in the pile and having the time of their lives.