> But then I realized, when you say the same sentence in plural - "they are doctors" - you don't have an article. You don't say "they are some doctors" (I had to Google, apparently "some" isn't an article anyway?)

That's just a historical quirk of the terminology. A(n) and the were named articles for no particular reason.

They belong to a much broader part of speech, called "determiners", and some is a determiner just like they are.