Mathew Yglesias summarizes his argument:
In particular, he argues that you can't say that specific elements of "Arab culture" account for the deficit because it's present in non-Arab countries as well. But you also can't say that specific elements of "Muslim culture" account for the deficit because it's not present in Muslim-majority countries that weren't part of the original Arab conquest:
And I think he's mostly right, but he puts too many countries in the wrong category. Turkey was not conquered by Arab armies, but by Turks. Pakistan was briefly conquered by Arab armies, but then spent most of its history under non-Arab dynasties.
I suspect the variable he's seeking is not "conquered by Arab armies" but "spent over 500 years ruled by a Caliphate dynasty". Which does seem to correlate better with a 21st century democracy deficit.