Broadly speaking, all existentialism was leftist in character because its core tenet was a rejection of old ways. Definitionally, you cannot reject the old order without being liberal/progressive/leftist/etc. Which, again, was in response to the 15-20 million killed during WWI, the most deadly 4 years in Europe since the plague years.

Again, I think you're inverting causality by blaming Marxism for post-modernism, when they are instead related results of the same overall trend, that was simply catalyzed by WWI (there's definitely a read on e.g. the 1917 Russian Revolution that it happens at least wildly differently without Tsarist Russia entering the war).