But in this case what do we base being a female on? It's more that possible she has 2 X chromosomes and is therefore a female in that sense
Well for one thing she has testes and not ovaries which suggests she had the Y chromosome. Second, she wasn't born female, she was raised female but has testes, it's really that simple.
If she was a 'normal' female athlete with those testosterone levels she would be deemed cheating and thrown out with an unfair performance advantage. Because she was born with male hormone levels but female genitalia, we ignore this entirely? We can't have a reasonable split of women/mens sports when the most important performance differentiator between the sexes is testosterone, then let people with male levels compete with the women.
The exact reason we have lets say a women's 100m sprint race is because women with lower test can't compete with men in that event. Thus we have men's and women's, which could have always been named, high and low testosterone events because ultimately that is what they are.
If you let people with high test compete in the women's or low testosterone category, you are making that entire category completely unbalanced and unfair. It is no different to allowing a drug cheat to compete, while the reason for high test would be different, the result is dominant competitors to which other women with normal test levels can't beat at all. So allowing people like Semenya to compete in the women's category, is pretty much telling the 100k's of female athletes around the globe and thousand that make it to the olympics, that it's all pointless because someone with three times their testosterone will definitely win all the events. It will kill the women's side of really any sport that allows it.
Would we watch F1 if 9 teams had V6 hybrids with ~900bhp but one team was allowed a V10 hybrid with 1300bhp? Nope. Would we watch a race in which 9 athletes had to run 100m but the 10th athlete gets to run only 85m, nope. Would we watch tennis if in singles one guys shots count as in using the doubles court lines while the other has to use singles?
Fairness in sport is a fundamental part of making it good to watch, an unfair match in which the winner is assured every time removes the competition.