Depends on the cat - https://www.cats.org.uk/news/meet-bellini-the-hermaphrodite-kitten-looking-for-a-new-home - but if you're in agreement that, say, a neutered cat still has a sex then you're in agreement with the idea that sex is not defined by gamete production.

Not sure why you're discussing the brain here, which is not something this article is about. But you'll be pleased to know that I call out neurosexism - the idea that brains are fundamentally different depending on sex - in my article "On Truly Changing Sex" - https://medium.com/@kim-hipwell/on-truly-changing-sex-a7770e903810