No biologist is an essentialist for long. Sorry, the author makes a good argument that there are only two sexes if and only if you ou define sex by the specific definition of gametes. The author is not wrong within that limited scope. But, what really matters is the phenotype of sex, which is not binary, is highly overlapping, and is a complex developmental phenomenon.
When people get all up in arms being anti trans, they are not getting up in arms about people not respecting the gametes... They are getting up in arms because they don't like it that the expression of sex phenotypes is heterogenous, overlapping, and scary, and that makes their small minds feel funny. Because they want to pretend that the world can be categorized into simple boxes that alleviate their anxiety, and gives them a sense of control. No, they don't even fucking know what a gamete is, for the most, and we sure as hell didn't know 200 years ago.
If you want to define biological sex as only being the gametes, fine. But that is a small thing. It's a definition that has little relevance. All the phenotypic variability in the expressed biology, phenotypic expression that depends on multifactorial developmental processes that can go in any of a billion different directions, that, while informed by sex chromosomes, are also affected by other non sex chromosomes genes, and also from variability in environmental exposures, which can affect the timing and dosing of sex hormones during development that actually DIFFERENTIATES thr biology? This article, and your perspective, only finds solid ground by limiting what biological sex encompasses to such a small piece of territory, that ceding that kingdom loses nothing meaningful, certainly not in how bodies are made, how sex is expressed and lived in, and to what matters in shaping their lives, personalities, who they feel akin to, and everything else. Have the gamete, who gives a shit? Get it?