I'm guessing the math was taking the total amount spent divided by how much it cost to power a house for a year with solar energy, which doesn't really say anything. Good intention, bad execution.
I think the essential point is, rather, instead of being destructive abroad, we could be productive at home. We could use our resources to improve life here instead of being complicit in taking the lives of others.
Pretty cool mirror symmetry with solar above and carbon cloud below. That is also an impressive way to convey the information along with the stats. Good symbol design.
[...] military spending, social spending, the economy, tax revenue, debt, and the money supply are all related to one another. This implies statistical models that estimate the effect of military spending on social spending or on the economy without considering the ways in which these variables affect and are affected by one another likely are misspecified.
[...] we find that military spending has a nonlinear effect on economic growth that varies over time. Increasing military spending leads to significantly lower GDP growth in the first three to six months following the increase and then significantly higher economic growth starting approximately one year after the increase.
How is "this" an oversimplification exactly? Yes, there is an interrelationship between the factors you quote. Yes, short-term spending on the military might improve the economy initially, but, like the quote says, the effect is nonlinear and inhibits growth in the long run.
Your quote supports rather than refutes the claim of this activist infographic. I would have to delve deeper into their sourcing, but the position is still strong overall.
Instead of using war to stimulate the economy, a Green New Deal could and the benefit would be sustained long term. It just takes large-scale leadership.