Only country that fits the description of Chinese dominated but not Chinese is Singapore.
That is the problem, the Chinese view is that ethnic Chinese is Chinese. The word Chinese has double meaning and get muddle up a lot. Unfortunately there doesn't seems to be another accepted English word for ethnic Chinese.
Huh?
Kuomintang for a long time considered themselves a "tru Chinese", carriers of the spirit of the Chinese nation (as opposd to those godless commies).