He's not completely right, and (as with any essay this length) it contains numerous inevitable simplifications. However, the generalized Darwinism from which Dawkins draws inspiration is still a powerful idea. I read Dawkins's book The Selfish Gene when I was in high school, and it's had a pretty deep and enduring influence on the way I think. This post of mine from last year, for example, comes around to a fairly Dawkinsian conclusion at the end.
The MeFi comments also turn up Dawkins's article from Sept. 15, 2001. A bit over-the-top, but nevertheless a useful, and all-too-rare, counterweight to the ridiculous band of crypto-theocrats currently running our country. Could anyone publish such a blunt article in a major American newspaper? Doubtful. As Nabokov wrote, in 1956, in the essay "On a Book Entitled Lolita":
[The publishers'] refusal to buy the book was based not on my treatment of the theme but on the theme itself, for there are at least three themes which are utterly taboo as far as most American publishers are concerned. The two others are: a Negro-White marriage which is a complete and glorious success resulting in lots of children and grandchildren; and the total atheist who lives a happy and useful life, and dies in his sleep at the age of 106.