But you're also wrong on two counts:

First, he wrote this and did most of his work at a time when power structures were clearly right wing. But the mechanisms he describes are universal and independent of the labels used by those in power: authoritarians will strongly conform to the dominant ideology, and social dominants will pretend to adhere to it to gain power. He just used the labels reflecting the situation at the time.

Second, he specifically points out that authoritarians in the Soviet Unions were nominally left wing.

Consider that this kind of shift in dominant ideology is a slow process, on a period longer that one academic's career.