He never mentions atheists and never uses the word faith at all.

Granted, but he uses thanking God and believing that life has a purpose as examples of the delusional thinking that he says we need to abandon -- implying that there can be no truth or substance to such beliefs. Can we call it a subtext that I painted in primary colours here?

I think there is very little alternative to faith in such cases. So far from being a caveman's delusion, it's the only thing we have.

Just so. Any system of belief or thought, even math, derives from at least one axiom (usually more than one). And by definition, there is no way to deduce the truth of an axiom. You have to choose your starting point based on what boils down to faith.

To reject someone else's axioms on the basis of your own, is at the heart of intolerance, religious or otherwise.