I looked at both of those.
The first is conflating Sex and Gender. As I said, sex isn’t defined by chromosomes and specific genes. It is partially determined by them, and other factors, such as in you temperature dependent example. But again Male and Female are terms used throughout all sexually reproducing lifeforms. Not just Humans. The terms are defined by the reproductive role of the animals gametes; not their genes or anatomy or anything else.

The Beyond XX & XY chart you provided shows a whole host of genetic disorders that can result in a range of outcomes that mix male and female traits in humans. Then it tries to assign genders onto those mixes of traits. But gender isn’t determined by genes, or anatomy. It’s determined by society and social convention. Do you see what I’m saying?

The statement “She is male” is consistent with a separation of gender from sex. It does leave an open question as to the use of Man and Woman. I’m torn on that one myself. Traditionally Man and Woman are terms of sex, while Masculine and Feminine are terms of gender. My first impulse is to maintain that. But calling her a man, seems different than calling her a male. So I can see changing man and woman to terms of gender, while keeping male and female as terms of sex. I’m not sure we really need a separate word for “human male” anyway. Most of the time there’s plenty of context to indicate if we’re talking about humans or other animals.