I'm not sure what "quantitative mysticism" means, but I'm not proposing anything quite so social-science-waffle sounding.
The article is not hardcore econophysics though, but basically a little bit of regression and then deference to physics without any economics.
Obviously the economy would be affected. But would it die forever?
1. Continued economic growth requires continued increased energy use.
2. Any energy source will eventually generate so much waste heat that the planet becomes uninhabitable.
3. Therefore, sustained economic growth is impossible.
How could the economy possibly plow through and ignore the physical limitations of the Earth? The author anticipates one might argue a larger portion of the economy goes to services of various points but suggests reasons this is implausible.
The best and most resilient example I know is the Black-Scholes equation - a framework to model option prices - based on a heat diffusion equation. Thing is, now it's never used with its original assumptions, but rather with a bunch of fixes. Oh, volatility isn't constant as we thought, let's add stochastic volatility. Oh, stock pricess are fat tailed and don't behave according to a geometric brownian motion, let's add discontinous jumps. Not to mention, that nobody uses historic volatility anymore. A hack of hack of a hack. So much, in fact, that the original elegant theory has just become a sort of convention, how everybody does their calculations.
I really don't understand the argument that laws that have been proven to work in one domain should work in another. I think it's a kind of quantitative mysticism.