Socialism is government ownership of the means of production (land and capital equipment). Nazi Germany retained private ownership of these things under government direction of their use.
Public direction of privately held means of production is the essence of fascism, both in Italy, in Germany, and in Roosevelt's failed New Deal schemes for the industry in the NRA and agirculture in the AAA.
Perhaps more accurately, we need to say that fascism is a leftist system that is antithetical to the rightist Anglo-American free enterprise system.
Hitler was a man of the left and the englightenment.
That point was made in the article. Would you care to explain to me the difference between the state ownership and complete state control? I suggest that it is a destinction without merit.