To get terminology out of the way, they are building towards Communism through Socialism, ie an economy where public ownership is the principle aspect of the economy. In other words, large firms and key industries are overwhelmingly publicly owned, so the Bourgeoisie doesn't have power over the state.
Now that terms are out of the way, you're correct, China does have billionaires. Even though that number is decreasing in recent years while working class purchasing power and wages are rising, that isn't enough of an answer as to why they still exist. Billionaires represent a contradiction the CPC must resolve. But how is the best way to go about that? What time scale? The CPC's role is to gradually resolve contradictions within Socialism in favor of the Proletariat in any inter-class dispute. They have to erase the foundations for billionaires, not the billionaires themselves.
I recommend checking out China Has Billionaires. The important thing to understand is that contradictions exist in all systems, and it is the process of working out these contradictions that provides room for advancement.
Rhetorically and factually trounce, then? Destroy, in the marketplace of ideas? What term would you prefer to describe your use as a springboard for me to bounce pro-Marxist ideas off of?
Its run by the communist party, whose purpose is guiding the country to communism and self dissolution; which has necessitated not skipping over the industrial and consumer revolutions, both of which likely require capitalism, but in any case have been done with capitalism so that path is easier and known, allowing them to benefit from the waste from less competent countries.
Or in other words, they're the only country in history to execute billionaires, whatever they are is objectively better than the US or EU.
Dialectics in this context refers to the aspects within the Marxist philosophy of Dialectical Materialism for the analysis of contradictions, and the direction they are resolved in. Billionaires within Socialism are a contradiction, therefore whether the state supports or works towards eliminating the foundations for them is what needs to be analyzed. I answered in another comment more about that.