Dawkins is not arguing that there is some particular gene that makes us selfish. Nor, that genes in general make us selfish. That is an unfortunate implication of the title.
Rather, he is intrigued by the notion of seemingly selfless acts, and he reasons from a gene selection basis for how such behavior could be selected for.
The author spends many words to disabuse the reader from the notions of "group selection" (for the good of the species), and even "individual selection" (survival of the fittest individuals). He makes a fairly strong argument that only "genes" (one or more "cistrons" - sections of genetic code) can be selected. He makes effective use of game theory to show how to derive the end results of various strategies for animal behavior (although these "strategies" are usually instinctual).
That said, Dawkins cannot help but editorialize and assert his own views on origins. On page 1, he is so bold as to quote another (in total agreement),
"... all attempts to answer that question ["What is man?"] before 1859 [referring to Darwin's "Origin of the Species"] are worthless and that we will be better off if we ignore them completely"So what is Dawkins' theology (and teleology)? Who is Dawkins' god?
Dawkins is no fan of anyone or anything (save his own thoughts). But I would argue that the closest thing to a god for him would be genes. He refers to them as "immortal", and attributes great power to them (although not omnipotence).
Even against this god of his own creation he cannot help but rebel. On page 201 he says, "We, alone on earth, can rebel against the tyranny of the selfish replicators."