I think we could sum up the argument like this:

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 simple answer is: by expanding beyond Earth. Achievable right now: putting computers in orbit.

I suppose that's a possibility but we're a pretty long way from having space colonies and it's not entirely clear how we would power such an endeavor.

It's not entirely clear when and how we'll hit the theoretical limit of power usage either, particularly if efficiency keeps increasing. All this discussion is about hypothetical situations.