Facilities operate under the flag of whatever country built them. Of course it's complicated because there's also no police there, so everything's legal unless somebody wants to report it. Even then they would have problems because they wouldn't be any actual evidence. At least not without sending an investigation team that to the Antarctic which they're unlikely to do.

Realistically I think it probably exists in a sort of gray zone which operates mostly on a don't commit any crime too bad rule. Don't be murdering people and you'll probably be okay doing whatever. After all, a certain amount of leniency is required because the world does not have an overabundance of people willing to live in Antarctica.