Having a degree in history...this person's wrong on a lot of major points. Not misinterpreting the facts, just plain wrong.
First off, monarchies aren't some sort of grand, unifying thing among the majority of human societies. For most of our existence as a species, we've been organized on the local level into bands centered around a familial group. At higher levels, you had tribes that were united based on the idea that they were all related. Usually the shared ancestry was so far back in time that it was probably mostly mythological, but you can see a pretty obvious organizing principle. Local bands might have had temporary leaders, and they probably all had people who had more or less influence, but there probably was no formal organization at all. Tribes didn't have any overarching political structure. The other members could probably influence the behavior of subgroups, and some likely held more sway than others because they were more powerful, but tribes weren't like countries. There was no governing body, much less a king. Even in historical times, most of the world still functioned that way.
Monarchies emerge at a very high level of social stratification. The fact that so many of history's most powerful societies were ruled by a monarch isn't *why* they were so successful. It's a consequence of that success. Groups that developed monarchs had to have urban centers that could serve as nexuses for government authority. That would that require agriculture, for the most part, but agriculture isn't sufficient. For one person to govern thousands, you have to have tight-knit and established trade routes, typically written language, and the ability to form armies or other force multipliers that allow the governing monarch to impose their will on the people. If the monarch controls more than one city, then that requires the ability to subdue your neighbors.
And, of course, not all societies that have reached that level of development form monarchies. The guy quoted in the OP mentions Rome, but Rome explicitly stopped having monarchs before most of its greatest early accomplishments. Other significant examples, like Democratic Athens or other Greek city-states that functioned as oligarchies just get glossed over here. Even once Rome became an empire and had a single ruler who could fairly be called a monarch, there was an aversion toward acknowledging that fact. There was a sense, in theory more than in practice, that the emperor was preserving a popular order. Struggles over the ruling role were the source of some of the Roman Empire's most significant internal conflicts, too, including some that Rome survived only by the skin of its teeth. There really weren't that many periods when Rome was stable and healthy under the rule of a single emperor, with minimal conflicts with the vestiges of republican government (the Senate was, well, still a thing; the powerful senatorial lines' fear of Caesar holding monarchic power is what got that motherfucker *stabbed*). They're seen as pretty remarkable as a result. It's true that some of Rome's "golden ages" happened under an emperor, but if you're going to hold up the Reign of the Good Emperors as an example of monarchy's success...well, what about the Crisis of the Third Century? Part of ending it involved the emperor splitting rule between multiple people.
Even at the height of monarchy in Europe in the Middle Ages, a lot of states that were under one ruler on paper were in reality patchworks. Rule in a given area might have fallen to a feudal lord, or an ecclesiastical leader (like a bishop), or a city government might have held sway. Multiple groups might have had different rights over one person or place in that patchwork, and their fealty to a distant king was often more ritualized and formal than real. True absolute monarchies start to show up again in Europe only in the Early Modern Period (although monarchs were still often limited in their power by laws forged together with local rulers centuries earlier, like the Magna Carta). Within a few centuries, the citizens of the more unified states that allowed absolute monarchy to exist started using the idea of the state as separate from the person of the monarch to limit or even get rid of the monarch's power.
Peasants and burghers (people who lived in towns and worked mainly as merchants or artisans) saw the monarch as an allie at times simply because the highest levels of government were a sort of court of appeals against local authorities. In the best case scenario, the monarch would be more interested in preserving unity and order than in whatever petty local power struggles local feudal leaders saw as so important. A government by and for the people can fill that role more effectively, though.
And, of course, the idea that monarchy is an Earthly reflection of a celestial hierarchy is some absolute bullshit. It was propped up by philosophers who supported a ruling monarch and wanted their patronage, but it both requires the belief that a celestial hierarchy actually exists *and* flies in the face of the image of monarchy actually presented in Christianity's holy texts. While there are notes more supportive of monarchy, this view of monarchy as natural and divinely ordained ignores completely the fact that, in the Hebrew Scriptures, God doesn't fucking want the Israelites to have a king. He relents when they beg for one because all their neighbors have one, but he's pretty pissed. You can read almost anything you want into the Bible, but claiming that monarchy is a natural reflection of Heaven ignores the fact that the Israelites were clearly supposed to function like the ancestral Afrasian societies that they (in reality) evolved out of, with a sort of communal decision making based on divine commandments, with leaders who had absolute power based on some link to the divine emerging only in times of war or other crises, then falling back into the general society once the crisis passed. The Book of Judges is a text about these leaders, who lived in a mythological past before the (probably also mythological) United Monarchy of Israel and Judah. It probably reflects a reality about early Israelite society, though, given the similarity between its vision and the social structure of related groups.