No, the suggestion that fascism is defined by their nationalism is incorrect...
We again will look at the dictionary term:
http://dictionary.reference.com/browse/fascism
fas·cism ( P ) Pronunciation Key (fshzm)
n.
1. often Fascism
a. A system of government marked by centralization of authority under a dictator, stringent socioeconomic controls, suppression of the opposition through terror and censorship, and
typically a policy of belligerent nationalism and racism.
b. A political philosophy or movement based on or advocating such a system of government.
2. Oppressive, dictatorial control.
I have bolded and italicized the word that shows that this assumption that nationalism is the only defining factor and is ALWAYS present in fascism is a mistaken assumption....
Read again: typically...
This word does NOT mean ALWAYS...
Then read the second accepted definition (second definition means it is the second-most accepted contextual definition of the word the how it is used part of the thing...) and we will find that the terminology actually fits them well. Especially if you take into account that they realized that similarities do not make something the same and hence they created a new term...
It is truly hypocritical to redefine a word to fit your argument when speaking of actual accuracy of definition. It is laughable. You are on the wrong side of this one... I know you hate to admit that you made a mistake on your assumption of definition, but you have.