Please stop calling "a woman is a person who identifies as such" a fuzzy definition. It is to definition what "alternative fact" is to a fact.

Now, you are right that for the purposes of this event no one defined what a girl or a boy is. The reason it is so (as is the case with many other social conventions) is because neither the participants nor the organizers challenge the classification.

There is no doubt that had it been challenged strongly and frequently enough, the implicit definitions would become explicit and formal.