I don't think that the author assumes the causation that you mention. He says that growth is composed of two parts. One part depends on energy production/consu

I don't think that the author assumes the causation that you mention. He says that growth is composed of two parts. One part depends on energy production/consumption and the other part does not -- If you don't like the causation ''energy consumption implies growth'', his theory still holds if you assume that the second part is more important than the first. Because our ability to be energy-efficient is bounded (even if his numbers are imprecise it's difficult to argue against this -- as our stuff cannot be more than 100% efficient), it means that the part of growth that does not rely on energy must take a disproportionate share of the total growth if you look far enough into the future. It precisely seems to me that the assumptions he makes are remarkably minimal.