I am redating this post with some fresh comments.
I finally got the chance to listen to this. Holy cow, Dawkins says that if we are deluded, we would have died out long ago.
Let's take a look.
T = We believe in God.
D = We are deluded.
X (for extinct) = We would have long ago become extinct.
T -> D
D -> X
So the fact that theists have not long since become extinct effectively refutes the central claim of Dawkins' book.