Military spending still doesn’t increase the size of the overall economy. It only redirects resources. That isn’t wrong, necessarily, but that doesn’t that military spending grows the economy, it just redirects it from civilian goods and investments to military goods and investments. Theoretically, the money spent on the military would have either been spent or invested in the private sector if there was no military.
Military spending does more than merely redirect resources since it creates goods that would not be otherwise created. It was precisely military spending that ended the Depression not Roosevelt’s fiscal programs.
In an depression one of the critical factors is to stimulate more investment and it took the demands of WWII to do that. Part of it was the deficit spending no doubt.