I mean, sure, you can speculatively postulate that HG-like egalitarianism is possible in non-HG societies. But that goes against the overwhelming mass of evidence.
I don't know if existentialism qualifies as "political philosophy" or not, but if all philosophies are political, then I think existentialism fits that description.
"Once freedom lights its beacon in a man’s heart, the gods are powerless against him. It’s a matter between man and man, and it is for other men, and for them only, to let him go his gait, or to throttle him." -- Jean-Paul Sartre, The Flies
The overwhelming history of humans has been in egalitarian societies. Stating that humans innately prefer a hierarchical society is patently absurd when you look at the millions of years of human evolution where we most definitely weren't. The problem is that the article quotes conservative philosophy as a given scientific fact.
Conservatism is a very thinly veiled biological argument in favor of a hierarchical society, which is seen as just. The majority of the society is expected to be bottom feeders serving those above them, this is the right way of things.
The French revolution which overthrew the feudal lords was seen as a threat to conservatism. Capitalism was seen as a solution to the possibility that superiority might not be fully heritable.
However, conservatism inevitably leads to biological justifications, such as white nationalism and objections to inheritance taxes.
Conservatism is really a series of polemics against egalitarianism that intend to say that society is hierarchical and those that belong to the top are people who look and act like me.
On another note, the philosophy of libertarian socialism comes closest in modern day societies to egalitarianism.