Use of "Some" when referring to quantities

Why can't the writer just say "...employs 12 million people"?

Because it employs approximately 12 million people, not 12 million exactly.

See the third definition of some and the example sentence below it (Lexico.com).

some (DETERMINER):

(used with a number) approximately.

‘some thirty different languages are spoken’

They provide ten more example sentences in a drop-down list below the one given with the definition. Note that some is used as a determiner in your example sentence, not an adverb.

"...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.