How does that idea fit with real-world China which runs a state-capitalist economy under an authoritarian communist rule?China has done what needed to be done to realize what is an unprecedented economic miracle, especially considering it's a socialist country surrounded by a hostile capitalist world. They chose to be pragmatic and it worked incredibly well.
While China certainly has capitalists and bilionaires, they are kept in check. China also set a 2050 target to fully transition to socialism.
You are right though that authoritarianism seems to be a pre-condition both for communist and fascist regimes.
Every society has a ruling class. In fascist societies it's the military together with the capital, in liberal societies it's the bourgeoisie, in socialist societies it's the working class. Authoritarian societies use force to maintain order, liberal societies use the illusion of choice. When that doesn't work, they promptly revert to force as everyone else.