"The evidence for design in the universe is without dispute, at least if atheist Richard Dawkins is right. The challenge of atheist-physicalists is to account for this without resorting to a designer".

Are you sure you've got this right? Design implies a plan or a designer. Dawkins accepts APPARENT design, and does indeed attempt to explain it away by Darwinism and natural selection i.e. The Blind Watchmaker. Therefore I would say Dawkins does dispute design.