I'd have to read the book to be sure, of course, but from the article I am far from convinced. The basic thesis, that religion "evolved" from many gods, to one, to none, dates back to Victorian "progressive" ideas. (The book leaves out the usually proposed previous stage, that of animism, where people believed in the spirits of places and things but saw them as equals rather than gods.) At the time it was propounded, it seemed to fit what was known of history and what was happening then, but by now there are big facts in the way of it.
The first is that the theory of gradually fewer divinities was deduced from studying "primitive" peoples, making the usual mistake of assuming they are living fossils whose culture hasn't changed in the last hundred thousand years. That was all we had at the time, but since then some physical evidence has emerged, and what it points to is the exact opposite. We have a collection of sculptures from ca. 10,000 years BP of nude female figures and abstractions which can be interpreted as such; there are no masculine equivalents. (There is a cave painting, known as "the Sorcerer," from the same period, which is usually copied as a male human figure with antlers, and which inspired Margaret Murray's theory of the ancient cult of the Horned God. But the transcription is controversial: the figure is painted, but the antlers are not, being either lightly scratched into the rock, or simply natural cracks which can be seen as horns with the eye of faith.)
We can't say for sure that these are idols: "religious item" is notoriously an archaeologist's term for "your guess is as good as mine." But unless they just prove the thesis that every new medium is first used for pornography, the best guess is that they are the first in a long line of Goddess figures that continued down to the Copper Age: and if they do represent a deity, then she was alone. Barring The Sorcerer, the earliest figurine resembling an icthyphalic Frey dates from around 6000 BP. One can make at least as good a case for the theory that the earliest religion was monotheistic, and it was only later that the clash of cultures (possibly, as has been suggested, between the sedentary cultures of the Goddess and the nomadic patriarchial tribes that worshipped the Allfather) shattered monotheism into the sparkling shards of polytheistic pantheons.
The second fact that undermines the theory is that today, in the rationalistic heartland of Western atheism, religion is growing exponentially. And it's interesting that the author doesn't appear to have noticed this at all. It's mentioned that he comes from Lebanon: it's not mentioned what faith he grew up in, but I've found before that anyone with a background in the Abrahamic faiths, whether they still believe or not, tends to have a tunnel vision of religion that simply can't see anything that doesn't have the trappings of those faiths. I've lost count of the arguments with atheists where they've said flatly "All religions (believe in Heaven and Hell, want converts, have one holy book, et cetera,)" and just got confused when I say "Mine doesn't." So the growth of Paganism, which makes nonsense of his core thesis, probably isn't even on his radar.
The third flaw that I can see is the Darwinian theory that religion survives and grows because it promotes cultural stability, hence believers survive and those around them are converted by example. In the first place, if people held to their religion because it improves their survival chances, and change it if it doesn't, the Jews of Europe would have all converted in the last thousand years. In the second place, a Lebanese should know there is no correlation between religiosity and social order. When England was under its most moralistic and conformist religion, the Puritan Commonwealth, it wasn't a time of harmony and order but of chaos and corruption. In the third place, most national conversions to Christianity didn't come about by gradual missionary work, but by a ruler's fiat (from Constantine onwards.) And the evidence is that this was usually for political reasons (including Constantine,) not from the ruler's beliefs. If there is any memetic selection going on, Christianity "evolved" not because it promoted social cohesion, but because it made rulers more secure.
My thoughts so far...