I don't have a dog in this fight. If Trans women end up competing with CIswomen, I don't know whether that situation would be fair or unfair, and I leave that question to others. But I value logical consistency, and the author's position contains a contradiction that he doesn;t notice. If there really is no difference in the athletic prowess of men and women, as the author claims, there is no reason to have a separate category for women, which would require the abolition of that category, which would mean that transwomen would not be able to compete in that category. The only way you can justify having Transwomen compete with Ciswomen is to have everybody compete with each other.

Gender is a social construct, but biological sex is not. I hear from people I think are experts that it is biological sex that gives biological men and Trans women the physical advantages that require the creation of a separate competitive category for women. They may be wrong about this, but if so that would require us to abolish different competitions for men and women.