China cannot by any rational scale at all be called Communist any more. No country with dozens of private property billionaires can.
It is arguably not really even socialist anymore, as many Europeans countries are certainly more socialist at core.
China at present has a lot more in common with its own ancient history than the imported European notions of socialist/capitalist.
The Party still uses the rhetoric, of course, but they don’t really walk the walk.
China, down its long history, has mostly been governed by an alliance between an Emperor and the mandarins. Unfortunately, the mandarins, despite their posturing about Confucian ethics, tended to become incredibly corrupt and steal everything in sight.
The primary function of the Emperor in the system was to emerge periodically and clean the mandarins’ house for them, stomp all over the corrupt ones. Of course, the emperors tended to become corrupt themselves, often under the influence of court eneuchs, who provided an alternate power center.
At the moment China has no Emperor. The Party fills the role of the mandarins. Historically speaking, this is a highly unstable system, as there is no restraint on the greed and corruption of the Party members.
The tradition of corruption in China over the centuries will boggle a westerner. During WWII Kuomintang officials would embezzle funds so aggressively that entire armies starved to death. That was not at all unusual in Chinese history.
The wild card here may be the quiet growth of Christian faith in China. This could be the salt that finally stays the rot.
Other systems like Buddhism also touted the virtues of integrity, but only Christianity can back it up with an unconditional love offer.