Socialism

If we are to judge the PRC on Marxist lines, given that they are Marxist-Leninists, then they are already Socialist. The large firms and key industries of the PRC are already overwhelmingly under public control, while private enterprise is a mix of small corporations, sole proprietorships, and cooperatives, all of which would not be able to go away simply by making them illegal, and need to be developed out of.

That's a more classical interpretation of Marxism than the later Maoist era, which tried to achieve a fully publicly owned economy in an extremely underdeveloped economy. That's why Marx was such a stickler about developing the Productive Forces.

The proletariat will use its political supremacy to wrest, by degrees, all capital from the bourgeoisie, to centralise all instruments of production in the hands of the State, i. e., of the proletariat organised as the ruling class; and to increase the total of productive forces as rapidly as possible.

I want you to look at the bolded word. Why did Marx say by degree? Did he think on day 1, businesses named A-C are nationalized, day 2 businesses D-E, etc etc? No. Marx believed that it is through nationalizing of the large firms that would be done immediately, and gradually as the small firms develop, they too can be folded into the public sector. The path to eliminated Private Property isn't to make it illegal, but to develop out of it.

The essential condition for the existence, and for the sway of the bourgeois class, is the formation and augmentation of capital;[43] the condition for capital is wage-labour. Wage-labour rests exclusively on competition between the labourers. The advance of industry, whose involuntary promoter is the bourgeoisie, replaces the isolation of the labourers, due to competition, by their revolutionary combination, due to association. The development of Modern Industry, therefore, cuts from under its feet the very foundation on which the bourgeoisie produces and appropriates products. What the bourgeoisie, therefore, produces, above all, are its own grave-diggers. Its fall and the victory of the proletariat are equally inevitable.

This is why, in the previous paragraph, Marx described public seizure in degrees, but raising the level of the productive forces as rapidly as possible.

China does have Billionaires, but these billionaires do not control key industries, nor vast megacorps. The number of billionaires is actually shrinking in the last few years. Instead, large firms and key industries are publicly owned, and small firms are privately owned. This is Marxism.

If we are to judge the PRC on Anarchist lines, then no, they are certainly not Anarchists, but they aren't claiming to be, either.