Public control is a continuum rather than an on/off switch in my view. They are owned by the state which is nominally responsive to the public, albeit very indirectly. But, then again, much of our economy and laws are determined by unelected councils (the Fed, the SCOTUS, etc.).
China definitely has big market aspects and private ownership, but I also think this can be overstated.
There is still massive public ownership of major companies and banks in China and land in all urban areas is publicly owned as well.