As has been already pointed out, Dawkins’ argument is directed against the popular theistic assertion that since the universe couldn’t have come about on its own (something never really supported by more than ignorance in itself), god is needed as a creator. All that Dawkins now does is point out the self-defeating nature of this argument, in a logically cogent way: either one would have to have the same questions one has regarding the existence of the universe regarding the existence of god, or one would have to accept that if god can come into existence spontaneously/exist eternally/timelessly, then so could the universe; thus, either the argument doesn’t solve the problem at all and just ‘pushes it back’, or it fails to demonstrate the necessity of a creator god.
Besides, even if the argument did show god (or some creating entity) to be necessary, to show that this entity is something that bears some relation to the Christian (or any) deity is another task altogether, yet something that is always conveniently glossed over by theists. It might, for instance, just be a completely insentient, inanimate god-particle (not to be confused with that other god-particle!), that has some way of bootstrapping itself into existence (or exists eternally, timelessly, transcendentally, whatever your favourite gloss might be), whose mere existence causes the creation of a universe. Even if this were a genuinely supernatural phenomenon, i.e. in principle inexplicable through scientific means, doesn’t mean its son can turn water into wine; there’s quite a leap of unfounded assumptions there.
Sophistry and Illusion, are you by any chance familiar with Lee Smolin’s ‘fecund universes’-proposal? (Also known as cosmological natural selection.) In brief, Smolin attempts to answer the question of why our universe seems so uniquely fit for supporting life by proposing a mechanism by which universes can ‘give birth’ to daughter universes – through the creation of black holes --, whose fundamental constants (and thereby, whose laws of physics) may differ slightly from those in the mother universe. Thus, the multiverse becomes dominated by universes having the greatest capacity for self-reproduction – those that easily create black holes --, which also makes them hospitable to complex molecules, and thereby, life.
I’m not sure I put much stock in this hypothesis – in particular, there seems to be a need for a peculiar sort of top-level concept of multiverse-time in which this evolution supposedly takes place, something I’m not all that certain is consistent at all --, but it’s a bold and fascinating proposal nonetheless.