They don't define gender.
Take a moment to think about why this is.
They define sex.
They use the phrase "gender identity" without explaining what they mean by 'identify as' or what gender is, and how it relates to sex.
Gender is not sex.
But it is used like a magician's decoy: here it is, gender, we mean sex here, and here it is again, meaning something different from sex, and now once more we're back to conflating it with sex.
I've noted this TIME AND AGAIN that glossaries from the main trans'gender' organisations fail to provide a definition of gender.
They skip straight to 'gender identity', never quite explaining what gender means, if it isn't sex.
There is a reason that all of these organisations employ sleight of hand with this term. They need to switch between two opposing meanings without people noticing.
If gender means sex, then to fail to accept one's immutable reality is unquestionably a delusion. This means it is a psychological disorder that needs treating as such.
If gender means social stereotypes, then it is unrelated to sex and should never be confused with terms like male or female, nor should it require medical treatment.
If it means an internal psychological sense of ones reproductive sex, then the onus is upon science to prove its existence in each sex and quantify how it manifests. And, it still precludes a person with testes from being validated that they have a sense of their phantom ovaries without resorting back to being a medical disorder.
The reason that no definition is ever given is that any truthful possible explanation of gender destroys completely the assertion that transgender is a genuine, verifiable state.
A whole medical industry and social movement built upon a word 'gender' that IS NOT DEFINED by its proponents.
It's like watching a magic act when you can see how the trick works.