Kinda think we're saying pretty much the same thing. Though you seem to be reading something -- "body type, ..., something, something, ..., organized around ..." -- in between the lines that clearly isn't there --^ Incorrect.
..."male" and "female" are the definiendums and that "has the phenotype that produces small gametes" and "has the phenotype that produces large gametes", respectively, are corresponding definiens.
^ Correct.
But that "has the phenotype that produces ..." seems to be something of an idiosyncrasy of Parker & Lehtonen. Even if there may well be some justification for it. For example, a later publication by Lehtonen himself is more consistent with both popular, though reputable, dictionaries, and with the Oxford Dictionary of Biology:
Gamete Size
'Gamete Size' published in 'Encyclopedia of Evolutionary Psychological Science'
link.springer.com
Female gametes are larger than male gametes. This is not an empirical observation, but a definition: in a system with two markedly different gamete sizes, we define females to be the sex that produces the larger gametes and vice-versa for males (Parker et al. 1972) ...