I'm confused. China is not America.
When people say things like "US is a republic, not a democracy", they're using the archaic definition of "democracy" from 200 years ago. Modern English has a different definition.
But it's usually redundant, because all modern democracies are representative. Some have more direct democracy features than others (e.g. Switzerland, or some western US states with their public initiative process), but they're still fundamentally representative.
“Republic” alone is correct, but overly nonspecific; essentially any government that isn't a hereditary monarchy or similar system where government power isn't private and heritable is a republic.
> The definition of republic is 2000 years old.
Well, sure, there is a definition that old (older, actually), but the one you seem to be using (the colloquial American one referring specifically to a system of elected representatives) is much newer, peculiar to American non-technical usage, and equivalent to “democratic republic” and very close to “representative democracy” (differing only in that the latter can coexist with constitutional monarchy.)
There are many countries in the world that fulfill all these criteria without being republics. Canada would be the closest example - they have a constitution that limits democratic decision making, and they have people elect representatives rather than deciding on issues directly. But they're not a republic, solely because they have a monarch.
And what I’m trying to get at as one definition of democracy is the idea that policy should track majority preferences, totally aside from any structural features of the system that might make that likely. For example, someone arguing that a certain bill should pass because a majority of citizens support it is making an argument from this idea. That argument in itself is totally aside from whether the legislature is even elected by the citizens.