This is obviously the crux of the matter. Not amount of state intervention makes a state socialist in itself, I think we can all at least agree on that much. So the key distinguishing point, here, for defenders of China's socialist credentials, is the proletarian character of its government.
So, how does one distinguish a proletarian dictatorship from any other kind of political formation? And how specifically do these distinctions manifest them in the Chinese case? (Or, more broadly, in any of the surviving or defunct socialist states of the twentieth century.)
Well in this case, as in most cases, there's really only one other possible formation: capitalism. And we know exactly what a capitalist state looks like: it does not even pretend to communist. Everywhere that capitalism has overthrown the DotP in counter-revolution, an aggressive de-communistization has taken place. Massive selloffs of state industries, destruction of the welfare state, a large decrease in the quality of life of the working class and poor, the destruction of the socialist state forms (soviets, collectivized farms, city councils, party branches, etc), and an all-out attack on the legacy of the socialist era. We see lustration, or the destruction of statues and symbolism, and the smearing and corruption of the history and people from that era.
When people point to many of these events happening in China, they are greatly exaggerating their size and importance. Yes there were some privatizations, yes, the capitalist sector is sizeable, yes, the Party since Mao has a questionable relationship with the legacy of the Mao era.
In contrast, where the proletariat controls the state we see a different type of organization of society. The welfare state becomes more comprehensive, extending not merely into generalized medical care, but specialization for child care and maternity facilities, creches and clinics in communities for the poor. We see the formation of, and protection of, the basic structures of a socialist state: namely, "soviets," i.e. councils in society and industry that feed into the central state apparatus. We see the control of, at the very least, the commanding heights of the economy: heavy industries like transportation, oil and gas, and steel, and/or other related fields, including foreign exchange. We see the formation of socialist Ideological State Apparatuses, and all the other pieces of a socialist superstructure that could not exist without a socialist base to support it: socialist institutions of law that favor the working class and punish or repress the bourgeoisie, or provide them unfavorable terms as compared to working people (think about how that relationship is reversed in capitalism); socialist "civil society" that replaces those that reproduce capitalist ideology (here I refer to Communist Youth vs. Boy Scouts, to give one example), and the same priorities that extend into all the realms of culture, entertainment, and the arts. And finally, we see the leading role of the Communist Party, an institution that could not exist with massive proletarian support. There are 87 million members of the CCP, the vast, vast majority of whom are proletarian. Would they (could they?) continue to support a capitalist restoration government that claimed to rule in their name, in the name of socialism? Such a thing would not be possible.
And finally, there remains the question of this: if we can at least agree that a Proletarian Dictatorship existed at some point in China, then where did it go? Who can point to the moment that the Chinese socialist state was overthrown and the bourgeoisie returned to power, destroying the socialist state's forms and building its own capitalist state in turn? If the CCP somehow magically "slid" into capitalist restoration without a counter-revolution, then doesn't that suggest the opposite: that a capitalist state can "slide" into socialism? We know at the very least from Marx and Engels (and from subsequent history) that this is not possible. It goes against the Marxist conception of the state as a tool of violence and class dictatorship by whoever owns it. It goes against the dialectical conception of the movement of forms. And most importantly, it defies all objective definition. It becomes up to each person to decide when it "feels" like China returned to capitalism, and that is quite frankly a useless measure if we are to imagine that any of this matters outside of personal opinion, and I think to 1.2 billion people, it matters very much.