You've just described "people in power" world wide. It isn't unique to communism, or china.
A huge amount of their economy is state owned[0]
That alone is a tenant of marxism. I'm not particularly interested in "true scotsman" style argument regarding is China 'really communist', as you can easily make the case that the U.S isn't technically a democracy, but it doesn't get us anywhere. It's just an argument of semantics.
[0] http://en.wikipedia.org/wiki/List_of_State-owned_enterprises...