Interestingly, if you press the people making that claim for what they mean by "left", their answer boils down to "whatever is in Cthulhu's forward cone".

I think you could make a case for totalitarianism, too. During the interwar years, not only old-school aristocracy but also market democracy were in some sense seen as being doomed by history; fascism got a lot of its punch from being thought of as a viable alternative to state communism when the dominant ideologies of the pre-WWI scene were temporarily discredited. Now, of course, we tend to see fascism as right-wing, but I get the sense that that mostly has to do with the mainstream left's adoption of civil rights causes in the postwar era; at the time, it would have been seen (at least by its adherents) as a more syncretic position. I don't think you can call WWII an unambiguous win for market democracy, but I do think that it ended up looking a lot more viable in 1946 than it did in, say, 1933.