I don't think FOM will have much luck suing Turkmenistan Sports in Turkmenistan. So they'd have to go after some other part of the broadcast chain. But given that the Premier League has yet to stop the broadcast of games from 52e they might not have much luck there either.
Was it another rebroadcast of a Setanta channel? Then again this race was available for free on youtube in some countries, maybe the F1 rights holders let Turkmenistan have a freebie. Or perhaps the gym Turkmenistan Sports broadcasts a load of rubbish from was closed due to covid so they just had to show something else to fill the time?