As written, this appears to be stronger and more protective language than the property clause in our own Constitution, which just says property cannot be taken without just compensation.
Of course, the Chinese communists probably know, from our own example, that the recognition of private property rights doesn't necessarily limit the powers of the state; we are "free" to own property in the U.S., but government at all levels tells us how we can use it, and compels us to pay taxes on it for all time. Maybe I'm cynical, but it seems to me the ChiComs give up nothing by recognizing "private property."
Just as our government doesn't.
Property privately owned but government controled is one definition of fascism.