Does this paper show that Democratic Presidents have economic policies that lead to better GDP growth?

Paper: https://www.aeaweb.org/articles?id=10.1257/aer.20140913

I’m just a laymen and I see this paper touted as proof that Democrat presidents are better for the economy than Republicans. Specifically, that the causal chain runs from the President to economic performance.

However, looking at the variables they found to be correlated, these seem more like good luck than due to actual policy differences coming from the executive branch?

But again, I’m just a layman trying to make heads or tails of the paper.

Can anyone explain, in layman terms, what the paper actually says, and does it actually show that the policies of Democratic Presidents CAUSE a better performing economy?