If the definition of a thing is both that thing and other things that identify as that thing, what does 'identify as' mean and are there any other examples of words being defined in this way?
Actually yes, there are loads, but you probably won't be aware that that is how they are defined in relation to reality; i.e. dependent on identification. And you probably won't realise because most people don't go into too much about the relationship between words/data and reality, via human thought. Although you're going to get me started on being all academic about the philosophy now because that's my niche...
I'll give you an example to ponder though. Patterns. A pattern is a a regular and intelligible form or sequence discernible in the way in which something happens or is done. So imagine you're observing a sequence of numbers generated by an algorithm and you identify a pattern. You call it a pattern. It is a pattern.
Then you realise that the next numbers in the sequence are not as you expected. It is no longer a pattern; at least you can't say that it is because right now you can't see a pattern that includes those new numbers. But not only that, it ceases to have been a pattern when you previously thought it was.
And then some clever dick comes along and recognises the pattern in the algorithm's new numbers and voila, the whole thing is a pattern again, and has always been, even when it wasn't, and will continue to be until someone recognises that in fact Mrs. Clever Dick made an error in her calculations and the whole thing doesn't exist any more.
Anyway, like I said, loads of words - all, I would suggest - actually depend on a symbiotic relationship between reality and human observation, and of course that observation can come from the person experiencing the reality as well.
So yeah, a room full of women, to all intents and purposes when you simply want to address them all as "women", is usually based on some perception; if you then drill down into it and realise one of them had a penis all along, were they not all women? You took them to be. But then you discover this penis-owner is in fact XX chromosomed and it's a surgically created appendage, were they all women again? So that's the gist of it. Reality and the words we use to describe it depend largely on perception in that moment. Hence why when it doesn't really matter what's in someone's pants or there DNA it's probably A-okay to call them a woman when that is what they perceive themselves to be. Although of course not mandatory if that is not what you perceive them to be. It's a complicated negotiation, philosophically. But such is life.