No, the term "Nazi Party"refers to the National Socialist German Workers' Party. The term "Nazi" refers to an adherent to the ideology of Hitler Fascism. The NSDAP didn't typically refer to themselves with that term.

There's also a square/rectangle situation in play: all Nazis are fascists but not all fascists are Nazis. In this case, though, he's more on the square side of the comparison. The biggest departures from the ideology are the inclusion of religion and the lack of Lebensraum (at least at home; there's an ironic argument to be made about how his belief that Bibi is moving too slowly in Gaza indicates that he has an eye towards creating living-space for certain groups at the expense of others).