That's not anti trans, that's anti India Willoughby.
India Willoughby was a well known male journalist until late middle age before deciding to transition. India Willoughby has fathered three children. India Willoughby now appears to be spending retirement permanently online being aggressive and abusive towards women, JK Rowling first and foremost. Pink News has even quoted some of the abusive things India Willoughby has said to and about JK Rowling in the article you linked to, all of which were far more unacceptable than calling a male person a male (fact) fantasist (opinion).
India Willoughby also made a big song and dance on Twitter about rejecting a gender neutral toilet in an airport and going in search of a female only one to use, thus rather undermining the "we just want to pee" argument and demonstrating that if we build it (it being additional spaces for trans people), they will not come. Because the whole point is being in women's spaces, whether women are OK with that or not.
It's not transphobic to call a male person male. It's factual. And it's not abusive to hit back at someone who has been relentlessly harassing you on Twitter for literally years. It's a very understandable human reaction.
Finally, and perhaps most importantly, no, JK Rowling doesn't believe trans women are women. Neither do I. Neither do the majority of people. It is not transphobic to not believe trans women are women, any more than it is Islamophobic to not worship Allah.