After having read a lot of Dawkins, I would put the following gloss on the big overarching argument he has developed over the entirety of his oeuvre:

• P1 - The only argument for God worth taking seriously is as the intelligent designer of the complexities of life.

• P2 - The complexities of life are better explained by evolution than by God.

• C - Therefore there is no argument for God worth taking seriously.

He spends a lot of time on P2, but tends to take P1 as self-evident and therefore not requiring support, which is, to say the least, controversial.

The piece you quoted is a smaller-scale argument that supports the larger one:

• P1 - In general, things can only be created by things that are more complex than themselves.
• P2 - The one exception to P1 is through the process of evolution.
• P3 - The more complex something is, the less probable it is that it could come into existence without an adequate explanatory process.
• P4 - God must be maximally complex in order to have created the universe
• C - therefore God must be maximally improbable.

P2 and P4 strike me as the controversial premises here.

It's worth noting here that Dawkins' reputation is higher outside the philosophical and scientific communities than within them. It's generally understood, even among philosophers sympathetic to his conclusions, that his arguments are not particularly rigorous. His role in the world of ideas is as an influential popularizer of religious, philosophical and scientific ideas.

After having read a lot of Dawkins, I would put the following gloss on the big overarching argument he has developed over the entirety of his oeuvre:

• P1 - The only argument for God worth taking seriously is as the intelligent designer of the complexities of life.

• P2 - The complexities of life are better explained by evolution than by God.

• C - Therefore there is no argument for God worth taking seriously.

He spends a lot of time on P2, but tends to take P1 as self-evident and therefore not requiring support, which is, to say the least, controversial.

The piece you quoted is a more fine-grained argument parallel to the coarser one:

• P1 - In general, things can only be created by things that are more complex than themselves.
• P2 - The one exception to P1 is through the process of evolution.
• P3 - The more complex something is, the less probable it is that it could come into existence without an adequate explanatory process.
• P4 - God must be maximally complex in order to have created the universe
• C - therefore God must be maximally improbable.

P1/P2 and P4 strike me as the controversial premises here.

It's worth noting here that Dawkins' reputation is higher outside the philosophical and scientific communities than within them. It's generally understood, even among philosophers sympathetic to his conclusions, that his arguments are not particularly rigorous. His role in the world of ideas is as an influential popularizer of religious, philosophical and scientific concepts.