How did fascism take root in Italy, even though they were on the winning side of WW1?

To tack on a minor detail left out of the great answer linked here, Italy was on the 'winning' side of WWI but they really didn't 'win' much. The 1915 Treaty of London was the basis for Italy's entry into the war on the side of the Allies, and in that treaty they were promised LOTS of Austrian (and some German/Ottoman) land. Northern Dalmatia, Tyrol, Trieste, the entirety of Albania...basically all of the best parts of the Adriatic. These promises were important for getting Italy into the war; both sides in WW1 were courting Italy prior.

Brief description of the war for Italy; it was brutal. Incompetent leadership mixed with trench warfare in an alpine environment. A major Austrian offensive in 1917 nearly crushed the entire Italian war effort. So, to put it short, the average soldier worked hard and suffered much.

Jump to post-war; "When ... I knew they would not give us what we were entitled to ... I writhed on the floor. I knocked my head against the wall. I cried. I wanted to die."<---A quote from Vittorio Orlando, the Italian Foreign Minister at the Paris Peace Conference. Could not be true, but it sums up the attitude at least: Italy didn't get 90% of what it fought for. The Slavic areas were determined to be better off under a Kingdom of Yugoslavia, and Albania was granted independence. There was considerable fuming between Italy and Serbia, Montenegro over this (which led to the Treaty of Rapallo which isn't important for this question )

The militaristic elements of Italian society, especially ex-soldiers, felt cheated, at least in terms of national pride, and the economic chaos (outlined in the linked post) wasn't helping. So, to address just one part of the question, Italy probably shouldn't be considered a big 'winner' in the grand scheme of things. Obviously it wasn't broken up like the real losers, but considering the cost of the war to what Italy gained, there was deep discontent brewing in society.

Sources: (The First World War, John Keegan) (The End of the European Era, Felix Gilbert ) (i hope these are OK!)