You are referring to few “special economic zones” at the large coastal cities. Most of those “private” companies are owned by party functionaries. China has turned from a classic Communist economy to a semi-capitalist economy at the service for the state. This is similar to fascist economics. The vast back-land of China however is still a corrupt communist rat’s hole.
Regardless of their economics, China is still a Commie tyranny, with no democracy, no basic freedoms and a all powerful Government. They are Communist tyrants who have figured out to use capitalist tools to empower themselves.
This was already done by Lenin with his NEP in 1921. Would you call him a capitalist?
The NEP was a joke, as was every economic initiative ever proposed by any Russian in history. In the NEP, it was merely foreign investment propping up the early Soviet economy. China has a thriving capitalist economy and a growing middle class, making it one of the largest consumer societies in the world. And, in case you haven’t heard, much of the development is now in the interior, in places like Chon Qing, not just on the coast.