Intersex people are neither biologically male nor biologically female
This is flat out false, and shows you don't actually know what you're talking about. Intersex people are Males or Females that have an intersex condition. This means sex characteristics that are inconsistent with their biological sex. This is usually means underdeveloped genitalia (men with hidden testes or a vagina), abnormal chromosome patterns (XX males are a thing, XY Women are also a thing, see the SRY gene link in my previous comment), abnormal hormonal levels (usually leads to very high levels of breast cancer unfortunately), etc. But at the end of the day, if that SRY Gene is on (wherever it is located, 99.999% of the time on the Y chromosome), it means you are male, if its off, female.
But intersex people should still be allowed to compete
I agree, but competition in any sport or esport necessarily means a fair ruleset and playing field. Otherwise its not competition at all. What this means most of the time in traditional sport is sex-segregation (in stuff like pistol shooting or esports, Sex is almost certainly irrelevant) This is especially true in combat sports. Letting a male fight against a woman is literally organized violence against women. There's just no world where where that should be allowed.