There was a sense in the wider community, that lasted a long time, around this case that took it as proving that socialization was the only substantive difference between boys and girls. It was seen as proving the gender hypothesis, that gender consisted of things that are completely constructed, and it's only by significant social pressures (although apparently these can be very subtle) that boys and girls internalize these. Without those pressures we'd see no difference socially.
The discussion of gender identity does get fraught in part because we do have a sexual identity, or sense of unity with our body and our sexual desire etc. It's incorporated in our sense of who we are. And it is partly developed as we grow into adult bodies, and also in relation to the existence of the opposite sex. Biologically, we are a species with two sexes and our sense of who we are as sexually reproducing individuals is only understood biologically, and in terms of meaning, in a kind of tension.
Gender identity is not real because it's based on a false premise, it's the wrong question and the wrong answer.We are sexed beings, physiologically, we know ourselves as sexed beings intellectually and in terms of intellectual system building, we are also cultural beings and so that knowledge is reflected in culture.