"...the fishing industry employs some 12 million people."
is perfectly grammatical. It is surely how one uses the word 'some' to say 'approximately'.
However, I similarly sense a strangeness to the usage of this slightly off-brand version of 'some'. I can't quite place the exact style it is common to but it reminds me slightly of children's literature. There are other adjectives that I could associate with this: 'but', 'certain'
"I have but one life to live"
where 'but' means 'only'.
"She has a certain 'je ne sais quoi' "
where 'certain' means 'particular'
These all sound like strange, not exactly misuses, but a bit outside of the normal meaning of the word with no obvious metaphor.
But style is often opinionated. So I can't really say the choice is wrong. The New Yorker's insistence on avoiding split infinitives often gives ungainly sentences, and sticking with the split would undoubtedly give a more felicitous reading, but hey, they're the New Yorker, and it's their stuff. I can only complain.