Levels of Topic in Liberal Fascism
There is political philosophy and intellectual and social history in the book. The book reports some history and uses it in a philosophical analysis. Therefore, it's difficult to understand the book if you don't discern these levels.
In this connection, I'll revise the taxonomy of totalitarianism that I presented below. I still maintain that "fascism," as a term in political philosophy, is totalitarianism with a cult of personality. But there is also the historical fact that "fascist" is a proper noun referring to certain regimes of the 20th Century. Let's give this usage a capital "F": "Fascist". This ambiguity can create confusion, as certain states that follow fascist ideals are not amongst the Fascist states.
Here is how to resolve the confusion. The Fascist states were particular implementations of fascism. There were other implementations (including the Soviet Union, America during its fascist moment, etc.) Now, "fascism" has an etymology involving bundles and "fascia" that is specific to certain historical circumstances. It was used to name the regimes of those circumstances: the Fascists. It was also used to name the political philosophy of those regimes. As it turns out, this political philosophy is not significantly different from that of other regimes that are not Fascist regimes. That their implementations may be different shouldn't be allowed to obscure this point. One shouldn't mistake an interesting historical difference between two fascist regimes for an interesting philosophical difference. There is no interesting philosophical difference amongst any of the fascist regimes. But you might conclude otherwise if you make this mistake.
This taxonomy seems fitting:
3. totalitarianism (state power is pervasive, complete)
3.1.1. socialist fascism (Marxist fascism; the state should own the capital)
3.1.2. communist fascism (the state, the people, and the general will will become one, and private property will be eliminated)
3.1.3. corporatist fascism (state does not possess capital but merely controls it)
The fascist states - states embracing the fascist political philosophy - may subscribe to any or several of the three listed implementations: socialist, communist, and corporatist. They may aspire to a communist implementation but undertake socialist one provisionally to that end. They may aspire to a socialist implementation and undertake a corporatist one provisionally. To point out that one supposed implementation of fascism is different from the Fascists' implementation does nothing to refute the book's thesis that both were fascistic.