The point is the right doesn’t want the government regulating businesses, whereas the left does. Therefore the left is more authoritarian regarding regulation of business, just as the right is more authoritarian in regulating personal rights.
Preferring one authority over another isn’t the same as being anti-authoritarian. People who want complete capitalist dominance over society are not that different from people who want complete state control over society. Different organizational and legal structure, but same type of backwards moral reasoning.
I don’t really find that a meaningful distinction in the context of discussing whether far-right ideologies are capable of being anti-hierarchy.
Governmental hierarchy vs private sector hierarchy is the distinction. The existence of hierarchy does not define authoritarianism in government. Do you consider a head of the household an authoritarian government?