China is a communist country with elements of capitalistic markets baked in. But the capitalistic elements are mostly a facade. Underneath, the state retains full ownership and control of all business. The CCP runs all aspects of the government (including the courts/judges), and is the single entity that decides what directions the country (and it's businesses) will move in.
The CCP, who defacto owns everything and has ultimate final say on everything, has one leader that has the ultimate final say on _everything_, Xi Jinping.
So while the waters of CCP models feel warm and free, understand it's not organically like that.
While I get the point you're making (it should be pretty obvious to anyone who's held a newspaper), I think it's important regardless to point out that Chinese companies AFAIK aren't worker-owned or -controlled, so you can't exactly call it communism, either. And they obviously do not have a "free market capitalism", as you just discussed.
It's simply a highly authoritarian state then, I guess?
As such, the state owns everything in both countries, the only differences are to what extent they control things.
I wouldn't even call the USA a capitalist system anymore, the economy is so heavily regulated and interfered with. It's a "managed economy", like pretty much every other nation's economy in the present day.