The reason why it seems so strange is that both argumentations are built on fundamentally different axioms and if Aquinas would live he would also vigorously deny Dawkins's premises.
Because Dawkins & Co. have nothing than contempt for religious argumentations, the argumentation of Dawkins & Co. does not consider the metaphysical premises, on which Aquinas's assumptions are based, and which (metaphysical premises) could be taken as granted during the time Aquinas wrote his Summa.
Aquinas was firmly standing on Aristotle's philosophy and was therefore considered untouchable during the time
Aquinas's Summa were created. Now that we have a much better overview over the severe errors Aristotle introduced, we can take many of his propositions much more critically.
Aristotle remarked that there are words for individuals: "moon","Aristotle","Mount Everest";
words which are generic: "cat","dog","rock";
and adjectives like "good","red","beautiful", etc. The adjectives he called universals.
He asked why such words exists (the problem is called problem of universals). Why do people use such words if there are essentially only individuals? Every cat, dog, human, rock, whatever you find in nature, is inimitable. Aristotle believed that real things are representations or approximations of universals and we are only able to use generic terms
because universals are real existing ideas and independent from their representations,
and because we judge the likeness of a real thing with its universal.
Example: A cat may be a house-cat, a ozelot, a puma, a lion, a tiger. Let's say we learn a new language and he tell us the word "sotehu". He points to the different cats and we understand that he wants to tell us that "sotehu" means cattiness despite their completely different color, fur, stance and size.
It is a straightforward reason to assume: if this is true, we automatically understand if we will find the perfect representation of a universal. If you do not know this (as Dawkins demonstrated) you find this irritating from a modern perspective.
Worse, Dawkins demonstrated with his "rebuttal" that he understood the meaning of the argument. Yes, "stinking" is a universal which is fulfilled by representations of a sweaty foot, limburger and rotten fish. So there may exist a perfect stinking entity and no, it is not God, but more something likely to be encountered in the seven circles of hell.
Dawkins launched a bad counterargument.
Wittgenstein and others have attacked Aristotle and the idea of universals and the idea that language tells us facts above the world mercilessly and in my opinion convincingly. So no counterarguments needed, Aquinas did not survive the test of time.
Some problems that seem evident for a "prove of God" were not apparent for Aquinas. The "unmoved mover" and "the first cause" cause either an infinite regress (Who moved God ? Wo created God ?) or a violation of the premises (Everything has to move/be created). The reason is that Aquinas made a whole book of special pleading for God's uniqueness (which are also conclusions from this proves and yes, for modern minds it is begging the question).
God is eternal, unchangeable and the only instance where essence and itself is equal. He cannot be defined but contains every positive universal aspect (truth, goodness, omnipotent and omniscient), etc. As special pleading is allowed in case of God, the arguments did not sound bad in former times. In essence the Summa Theologiae is not philosophical, but a defense of the catholic belief based on Aristotle.
Your question is if the argument has any validity. Now, it is not a proof for God, but what about the idea of a maximum itself ? In fact the idea of perfection pervades still the modern era. People gets irritated if, e.g., a justice would say: "Ok, we as judges and prosecutors do a 9-5 job. We are trying to do a good job, but shit happens time from time." Or if a doctor would say:"You know, human rights has this idea of equality. But right now I have the president on the other table, he is rich, he is powerful and he has a broken hand. You on the other hand are a jobless, broken white trailer trash who was unfortunately hit by a bullet. So I ask you to bleed quietly until I have fixed the president's hand." It may be the whole truth, but people do not accept that.
People fought and died for ideals who do not exist as entities (freedom, equality, privacy, right of property....). If you deny that the argument itself is meritless, you must stick to the viewpoint that striving for a maximum or believing in the existence of a maximum is a stupid thing to think or do. And if it is a stupid thing, your idea of (e.g. "human rights") loses its plausibility. Hard question.