I really wish I had enough money to send all of the folks who believe that China is still "communist" on a trip to Shanghai or Guangzou to see the thriving private-sector economy that has been flourishing for over a decade. I'll let the Birchers continue to believe their mythology about contemporary China in the meantime.
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?