Fascism is an authoritarian political ideology that promotes the community before the individual and utilizes a mixed economy referred to as "the third way". It's a collectivist ideology.
That is Progressivism to a T.
Fascism got the label of "right wing" because of it's "opposition" to Communism. The reality is that Communism and Fascism aren't all that different and most of the Nazi Youth's were Communists before they were fascists and that the "opposition" came because Fascists and Communists were competing for the same supporters.
The "Right Wing" label, especially in American Political Terms, is obviously not appropriate to any reasonable evaluation of the word. The "Right/Left" wing label comes from the French Revolution where Reactionaries were Right Wing and Revolutionaries Left Wing. In America, the Reactionaries are "Classical Liberals" (today called Libertarians) while the Revolutionaries are "Neo (FDR) Liberals, Socialists and Communists". (Note even the definition you provide notes an opposition to "liberalism"). Therefore, in the American Right/Left axis, Fascism would be soundly Left Wing (which is why I argue Neoconservatism isn't a Right Wing ideology).
Furthermore look at the economics of Germany, the Welfare State (you know, like we have now) stems from Bismark's economic policies that Hitler sought to replicate. Regulation of industry was a fascist/corportist concept (the idea being that businesses were private, but they had to follow the instructions and rules of teh government - thus the title of the "third way" between socialism and (true, lassiez-faire capitalism).
