Billionaires are bourgeoisie. The existence of the bourgeoisie does not mean a system is capitalist alone, what's important is what is the principal aspect of the economy. You're relying on the "one-drop" rule, which would imply that the existence of a public post office in the US means that the US is fully communist. That's obviously ridiculous, private ownership is the principal aspect of the Statesian economy, but this is the limit of the "one-drop" rule.

Capitalism is a mode of production, not a class. I am not defending the permanent existence of the bourgeoisie, but instead defending a system where the bourgeoisie is waning and socialized production is rising. I am defending the transitional status as valid and moving, not a static, unmoving snapshot.