China is a capitalist society governed by a communist party that enacts social democrat policies.
Capitalist society - the society, daily life, culture etc. Is dominated by commodities, efficiency, wage labor, etc.
Communist party - given by the history of the party and the current debates, discourse within the party.
Social democrat policies - the part that is most contentious I feel. But large scale schemes and programs like poverty allieviation, public infrastructure, literacy etc. are similar to what many past and present social-democrat, welfare, Keynesian etc countries and governments have done. Under this falls unions, minimum wage, overtime and other means of trying to direct capitalism in a more "gentle" manner.
This allows us to make certain predictions. As long as the society is dominated by capitalist relations, there cannot be any move towards communism. This also prevents socialism as that is, by definition, a move towards communism.
The presence of a communist party as the government prevents neoliberalism, austerity etc from taking control like they have in other social-democrat countries.
But the social democrat policies by themselves cannot prevent capitalism's ills which manifest itself in economic inequality, social unrest, burgeoning power of the bourgeoisie, and the rise of nationalistic, xenophobic elements.
Once again, the communist party prevents these from exploding out of control as they have in the West and in the capitalist global south.
The CPC has infront of it the unenviable task of transitioning a society from capitalism to socialism while fighting off revisionist, capitalist, and nationalist elements from within.
The criticisms of the party from the left then hinge on whether it is successfully fighting off these challenges, succumbing to them, or in a state of ceasefire.
The CPC needs to be helped in this fight by those of us outside of China in getting communist governments installed in our nations. But it needs help from within the country too from a bottoms-up socialist movement that ends capitalist relations in the community. If it fights alone, it will fail.