Gee! I thought Han-guk was Korean people, Chung-Guk is Chinese people, and Mi-guk is American people Hmmm, well I don't speak Korean, I was just repeating something I read once. So guk just means "people"? Could it be that they refer to themselves as "the people" for short?
No, it just morphed in everyday speech from hanguk to guk. Then got spelled phonetically.