ccp doesn't respect karl marx's teachings. instead they adopt Lenin's marxist-leninist like you said OP. it is a twisted version that has caused people to dislike 'communism' as a whole. But communism is just the end state of capitalism which eventually self implodes. It's something that happens naturally over a long period of time rather than being forced like Lenin's ideology which is more of a dictatorship. Technically any form of capitalism is part of 'marxism' as an ideology, since capitalism is a means to an end.