Literally once every 4 or 5 years I've heard a layman say "second world" referring to "poorer than America, richer than Ethiopia"; the lay usage is probably still first/third world, but people are slowly cottoning onto developed/developing nation.
I think even in common use, that use of "second world" is still "wrong," as far as anything in English can be wrong. Ted Cruz referred to it as a "basketball ring" and we all had a laugh, but we also all understood what he was talking about; is that wrong?
I'm mostly reluctant to tell anyone that their use of English is wrong, because it's such a fluid and ever-changing language; but when something like "second world" comes up and not in reference to the Soviet countries, it still jumps out at me as "well, that's not how people always used to use that phrase"...
An academic using that phrasing would certainly be wrong, but a layman?