I used Google translate to read the news report in the first link so there was probably quite a lot lost in translation so I'm not entirely clear what has happened.
Two people who either were or had been in a relationship got into a heated argument on Facebook and the defendant posted offensive messages to the claimant which referenced their gender ID. The claimant appears to be a TW but the sex of the defendant isn't mentioned, was it a female ex partner?
Is the crux of the matter correctly sexing the claimant or the nature of the remarks which related to gender ID?