I have read the full text of Damore's document, including the TL;DR at the front.
In my opinion he seems to be saying that you recruit someone on individual ability regardless of sex or race. But when you are judging company policies and their effectiveness you must use the science of statistics. Unfortunately, few politicians, managers, lawyers, journalists, or internet trolls understand the science of statistics. He even includes a graph to show how variability in any attribute between group A and group B will lead to both groups existing within an average sample, because of the overlap of the probability distributions. But extreme samples will be dominated by one group. The example I use with that graph is the average height of men and women.
Damore wrote a sincere, professional, and courteous document. To be fired for writing that is disgraceful, and I hope Google get legally hammered for their misdeed.
At one time el Reg might have understood his statistical arguments, but those days seem to be long gone.