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.