I think the guy has just got lost in his own model, which tries to liken such a complex thing as the human civbilisation with a simple physical system, employing a constant relationship between global energy use and the civilisation's accumulated economic productivity. This is just naive...
The laws of thermodynamics relate the incredibly complex interactions of unfathomable numbers of resonating particles to a handful of simple laws.
Is it not intuitively correct to assume that no system can grown limitless, that there must be an upper bound for everything?
No, it is not.
Then why does our economy need to grow all the time? Why can't we just be content with a very high output? Does it need to increase all the time? And worse, does the growth need to increase all the time?
Well it passes the time while we wait for the sun to explode. The problem really is that we measure growth by GDP. The easiest way to raise GDP is to open a factory employing half the population to make intricate gold figurines, then employ the other half of the population to smash them.