Oh boy, it's this argument again.
The only criteria for someone to be an exhibitionist is to have a desire of exposing themselves in public for the thrill of it. That's it. It doesn't matter if the exhibitionist is the type to shyly hide away out of embarrassment or the type to boldly show it all off, it's still exhibitionism either way because they're naked in public.
More accurately (if we are talking about the psychological definition) an exhibitionist is one with the
compulsion to show their genitals in public. It doesn't matter, as you say, whether they are shy or bold about it.
The non-psychological (i.e. "common English) definition is anyone who likes to draw attention to themselves by their behavior. In this definition, they are choosing to act this way. It's not a compulsion.
This game is using a well-trodden trope. I hope the dev can do something different and interesting in this trope. Another typical exhibitionist game will have a hard time selling itself with so much good competition.