To elaborate a bit: when I read the description, it sounds like a person could make the same claim about humanity: "there are billions of sexes: John, Jane, Tim, Judy, Juan, Maria, etc etc"
How is this different? Or equivalently, what makes a "sex" a "sex" if it's just variability within the sex chromosome, but every individual is able to create progeny with 25% (?) of other individuals.
To me, that sounds like 4 sexes.