ChattyLion I'm not a lawyer, but from reading some of the ECHR judgements, it appears that the court ruling is binding on the country which has been taken to the European Court, but not necessarily on other countries.
So the Goodwin v UK ruling was binding on the UK, to find a way in which a transsexual male could marry his male partner. This could have been solved by legislation allowing same sex marriage. There was another element about not being 'outed' at work as the same person who had previously worked for the same company as a man due to their NI number being the same. Again, another solution could have been found to this without the need to falsify the birth record.
This is from the most recent ruling I could find on gender recognition in the ECHR.
We note that it appears clearly from the factual findings made by the Court in the above-mentioned case of Hämäläinen v. Finland that there is no consensus among the European States on the question whether there is a right to have a new sex legally recognised and which conditions have to be fulfilled for such recognition.
It appears that there is no obligation on a European state to have a process for people to change their legally recognised sex.