[MattyDub]

I think you're missing the post's author's point. He isn't saying "after wars the DJIA goes up", he's saying "after periods of inflation, the DJIA goes up" (see the title of the graph).

Note he still doesn't mention 1929-1933, which seems like a big omission, although it doesn't directly contradict the assertion.

[6ren]

Interestingly, there is no CPI increase accompanying the present period. Maybe it's delayed a bit, as it was for WWII.