I think that the word 'fascist' is not well enough defined to have a clear meaning. I am inclined towards seeing it as almost entirely as authoritarianism, to the extent that I'm not sure that there's a reason for the word 'fascism' to exist at all. Authoritarianism is definitely the most important thing in fascism, which is fitting since it's named after a symbol of authority.
Other than nationalism, what if anything do you think defines fascism as being something different to other forms of authoritarianism?
That's an odd question to me (and I think it's assumed that our debate is in different tone than the "debate" we're both having with Zethor). The reason it's an odd question is because nationalism IS the most essential difference between fascism and some other forms of authoritarianism. If the Nazis had been "Internationalist Socialists" they'd have been communists with extra racism. However, there must logically be other distinctions as you point out. So for example, we have monarchies both contemporary and historically which are authoritarian but they are not fascist. At least not in my mind which I realise is important to add as the definition is what we're discussing. To support that though, I don't think any political theorist would describe Saudi Arabia as a fascist government. Although ideologues who treat it as a synonym for oppression might. There's also a cultural component which I hesitate to raise because it's a bit woolly, but feel I have to because despite that it seems to be a consistent presence. And that is the emphasis on hardship. The communists I know and much of the communist bumpf that I have read is all very utopian. I've had them tell me about how you wouldn't have to work more than X hours, etc. I'd need to immerse myself in historical literature to say if this is right or inadequate exposure but the pitch for fascism by Mussolini and by Hitler was very much about work, hardship and endurance. I think it might stem from the communists I know today to be all about overthrowing the capitalists who force us to work for them whereas in Weimar Germany with hyperinflation and economic disaster, the dream was to be able to work at a good job and earn a living wage and keep it. Communism of course has its "We can do it!" posters but one of the themes of fascism has always been Strength and Purity. Communism seems to emphasize more 'share everything for everybody'. The interesting thing with Hitler is he didn't do a Jeremy Corbyn and ponies for all. He stood up and promised discipline, suffering and the dignity of work. At least in much of his stuff. Again, this is cultural and an impression more than a definition so I wouldn't add it save that I feel it's part of it. Leaving aside the internationalist / nationalist divide, Communism seems "ponies for all" and Fascism seems "Ponies for the deserving".
The thing is, we have to distinguish between political models as intended vs. those in practice. We've only ever seen fascism as a reactive force. We've never seen it allowed to endure long term. For me the most fascinating thought experiment in this question is not whether Germany had won so much as if it had not been defeated. I'd love to know how long the Third Reich would have endured and how it would have changed or not. I think that Fascism might have a better chance of surviving long term than communism because (and Zethor is going to be frothing at this comment!

) fascism is less extreme than communism. I'd better explain. Communism is very utopian and doesn't allow for hierarchy of outcomes. Of course in the USSR there was, but the doctrine is one of no class. (In every sense!). Fascism is left wing, but it doesn't solely do away with the concept of class in that it believes in better and worse groups of people. Communists doctrinally needed to make everyone the same. The Nazis doctrinally wanted to be socialist
within their group. Which I suppose might be another way of saying nationalist.
Anyway, that was a long and ill-planned out comment. The answer to your question is probably in there between the lines somewhere, but it would take more work from me to formulate it better. Short version, the key distinguishing qualities of fascism as a particular form of authoritarianism are (imo):
- Nationalism
- Rejection of universal equality
- Socialist doctrine
- Social purity (racial in the Nazis case)
- Idealisation of individual strength and loyalty.
Second and fourth are intertwined really and are what will give Leftists conniptions when you call Fascism Left Wing. And also why they define Fascism as Right Wing and why more neutral political theorists define it as a fusion of Right Wing and Left Wing ideologies. It's extreme socialism with a defined (i.e. bounded) society.