I’m not defending this definition, but I will point out that gender has never been about the chromosomes you were born with. It has been about how people around you perceived you and people often have overly simplistic ideas about exactly what that meant.

Plus it’s totally normal for words to have more technical detail than they first appeared. The idea of a sex binary doesn’t fully exist so we’d need something to deal with that anyway.

I personally support segregation based on hormones as the fairest option available. Otherwise if you use purely a genetic test there are plenty of women with high t levels without an sry gene and no one disputes that high t levels confer a biological advantage in many sports

Going even further back, gender denoted, originally, a linguistical construct associated with sex but not strictly dependent on it, as seen on romance languages like Spanish, Portuguese, etc. [1] There, words have their own gender and, sometimes, the gender of the word and the sex/social gender of the subject may disagree. Ex.: "ant" in Spanish is "hormiga", but this noun is exclusively feminine with no masculine form.

[1] https://etymologyworld.com/item/gender