Nazi, rather National Socialist Workers' Party, can not be on the Right. Socialism is ALWAYS on the Left, just like communism.
Therefore, how could Nazism be associated with the Right with the word "Socialist" in the title? That doesn't make sense.
The original author leaves out some facts that don't support his line.
He says...Then the Reichstag [which was the "seat" of the German government, just like the our American equivalent, the U.S. Capitol building in Washington, D.C.] was blown up and Hitler ram-rodded an emergency anti-terrorist act through Parliament that gave the Gestapo extra-ordinary powers.....
Just a second. The Reichstag fire was blamed on Communists by the Nazis. Also there's that distinction about private property. Socialists/Communists want(ed) to totally get rid of it. Nazis didn't.
This is an interesting debate but I think it mainly depends on how you look [or were taught to look] at the political spectrum; as a half-arc, a circle (with communism and fascism meeting at the bottom) or something else.