Interesting.

Can someone explain in short sentences and small words why the author is so sure that the causation necessarily 100% goes:

Increasing GDP -> Increased Demand for Gov't -> Increased Gov't
and not
Increased Gov't spending -> Increased GDP

Because in this article, as I understand it, they seem to be presupposing that the first effect is dominant and the second effect is not present at all, while I would naively have expected both effects to be present.

A lot of government spending is things I would expect naively to stimulate the economy - every time the Gov't buy things from the market or employs people, that's more money flowing in the system and causing knock-on effects as people use their pay or revenue or whatever from gov't projects to employ other people. You can also consider a lot of social welfare stuff employs people, and education both employs people and makes more valuable employees. Note that I am not an economist - my understanding is at best a layman's.