You're going to get an extreme warmonger penalty from hitting either the CS or Korea's capital, so why would you take that penalty (when you've already met a couple other civs) when all you get out of it is terrible dirt?
Obviously, if he can take Korea capital, that's the target. However, generally speaking, far easier to take one CS than an Immortal AI with a tech lead. And Korea can be feisty if they build Hwacha. The CS left of Prague is the one to take, to set up 2 coastals. He could also have also planted another inland city on the river, but then can't produce a navy if he want one (that said, he doesn't need one). With his land, the "by the book" play is turtle with 3 or 4 (preferably 4 with Ethiopia), and then swallow Korea after Ideologies (leaving behind worst city), and maybe swallow some Spain, too.
Anyway, it is certainly far easier to Comp bow rush one CS than a Korean capital. Particularly as this Korea built Great Wall. Good luck with that. Particularly if he's learning Immortal. To each their own, but knocking out a CS early works, too.