Except that I don't disagree with the fact that biology is central. What I disagree with is his simplified view of biology. As the Nature article that I linked shows, sexual determination is more complex, there are biological reasons to not affirm simple gender binaries.
And if you read the article that I linked, you will see why that is too simple. There are XX and XY people that, due to other influences, do not feel like the gender assigned to the sexual function (and these can exhibit external physiological signs as well) because sexual determination is a more complex developmental process, that involves hormones and genetic networks and switches.
I will link it again:
http://www.nature.com/news/sex-redefined-1.16943
That is really all that I have to and want to show. Since the claim of Shapiro and the OP is that biology is clear, it is not. Understanding sexual development is a work in process, and it seems to be more complex than he claims it is. Whether this accounts for all cases or justifies further gender differentiation remains to be seen. I leave that to the experts, and Shapiro isn't one of them.