I don’t think that such radicalization requires a defeat. If it necessarily did, one might rather have expected that Hitler’s popularity should have skyrocketed soon after 1918. Instead, his rise was triggered by an economic crisis more then a decade after the war, the kind of event which has the potential to affect victors to a similar extent as the vanquished. Before it, the Nazis got something like 1% of the vote.
3% to 5%, basically, which was consistent across all the 1920s elections.
And as Faeelin says, Japan’s victory in WWI did not prevent it from developing a vile regime.
The same for Italy and Romania. Greece also developed a fairly thuggish dictatorship, despite being on the winning side.