I mean, they should but that does not appear to be the case. Here for instance:

Asked transgender activist Amrita Sarkar: “Why should rape laws which protect women be different from the rape laws that protect trans women? How can one offence be awarded a punishment of seven years to life while another merely six months to two years?”

I find it a difficult subject to look into because there aren't a lot of great English sources doing a direct analysis on how these laws are interpreted. I have no idea if the problem is a mismatch on ID or if the problem is that even if a trans woman were to have ID that reads "female" that she would still be considered "third-gender" under the law.

But of course, as you noted above, what does it matter if laws exist if they aren't enforced?

“The Indian constitution does not discriminate, but its keepers certainly do. Of the transgender people registered with us, at least one in four has been a victim of rape, gang-rape or serious sexual violence. And of these, only 10 per cent were successful in getting official complaints registered with the police. Most of them were deterred with the same question: you’re neither male nor female; how can you be raped?” Khan says.

Khushi was asked the same question when she tried to register an offence after she was raped by three policemen. Authorities at first refused to believe her gruesome tale of custodial torture, she says.