So, these countries' sodomy laws are doomed. Either their national courts or IACHR/CCJ/Privy Council will strike them down.

But will same-sex couples be able to marry after the ruling's publication, without changes to the Constitution and marriage laws?

That article makes no sense.
"Thursday’s ruling was in a case brought by a US-Romanian couple who had asked the authorities to recognise their marriage, registered in Belgium, so the American could move with his husband to Romania. The constitutional court based its judgment on a ruling issued in June by the Court of Justice of the European Union." — That ruling was issued on Wednesday, July 18 (here is the text, Google Translate help us: https://www.ccr.ro/files/products/decizia_534_201... ). Romanian CC was the very party that referred the Coman case to CJEU for an opinion, and after the ruling was issued by CJEU on June 5 Romanian CC issued a final ruling. CJEU ruling was based solely on the EU law, namely its freedom of movement directive, EU law doesn't regulate family/marriage law at all. And there is no need for a conservative court in a conservative country to step farther than CJEU stepped, even if the court was liberal it wouldn't want its ruling to inspire a new constitutional referendum that could punish the CC for its expressly pro-gay stance that wasn't induced by the evil, undemocratic, godless, lefty EU. If it was liberal it wouldn't want to rise the homophobic voter turnout at the upcoming October 7 same-sex marriage ban referendum by such a ruling as well.
We should understand that the both rulings do nothing at recognising gay couples' _family life_. Romanian family/marriage law was not touched by them. They just tell that due to EU law some persons are entitled to residency rights (and the freedom of movement within the EU) in Romania and, by the nature of the precedent, in several other EU member states.
Romanian CC's site doesn't mention such a ruling as was described in the article that was issued yesterday. There is a press release though dated September 27 but it is about a totally different ruling. I don't know why that was (mis)reported but sometimes such a mistakes happen to AFP, AP or Reuters.

I hope there won't be a referendum on that law.

I would support not abolishing the presence of a gender marker but making its presence optional, just like there are optional marks in some identity documents for height, ethnicity or blood type that may be useful for identification or other purposes. And even if some persons wouldn't have a gender marker on their IDs it doesn't mean that the other people couldn't address them in the gender deduced from their (non)conformance to gender stereotypes, the way it has always been. You don't have to look at the someone's papers in order to call them "sir" or "madam".

The coolest option would be removal of the mandatory nature of the sex/gender field in identity documents.

The person quoted in that article is a spokesman of neither Indian National Congress political party nor of the Indian Parliament, but of a paramilitary organisation linked to the governing party.

So, no matter how liberal and progressive California is, it still sucks to be gay there if you are being incarcerated?

It's strange that he didn't also sue all the members of the legislature who voted in favor of the antidiscrimination law.

Jack Phillips is being persecuted? Well, I hope that in the worst case the poor guy at least will get asylum somewhere. In Russia, for example.