It isn't as much as a replacement term, but you make a fair point that is doesn't translate well. It is both jargon and a loaded concept, which can be confusing when taken literally and without understanding what it aims to represent.
Funnily enough until they said their country was such, I assumed they were American saying 'global' South to distinguish from meaning a South American country.
'Southern hemisphere' is fine though I think? And I assume that's what was meant.
If they meant it as a replacement for "third world" (in the contemporary sense, not explicitly about the cold war), then they didn't mean anything to do with south as a direction.
I'm not against replacing "third world", but something with the word "south" is ambiguous and counterintuitive.