Many countries include ‘Democratic’ or ‘People’s’ in their names, even though they are not democratic and do not serve their people. Examples: Democratic People’s Republic of Korea Lao People’s Democratic Republic People’s Democratic Republic of Algeria Democratic Republic of the Congo And German Democratic Republic (East Side) in 1949–1990. None of these states are democratic, power and wealth are concentrated in the hands of a small ruling elite. Who are they fooling with these names?
It sounds like that Chinese phrase is better translated as “republic”, then, as the definition you give is almost exactly equivalent. Republic and democracy aren’t synonymous in western political thought, although they’re often linked and conflated.