"So you're nearly right. The economy is limited by the resources available to us on this planet. One day, no matter how careful we are here with our resources on earth, we'll have to go off and mine some asteroids, etc."
Not quite. The "size" of the economy (and Worstall, probably for didactic reasons, plays fast and loose with the term 'wealth' in this article) is its output, i.e. the value of goods and services produced in a year. This is found simply by multiplying the number of people by how much each person produces (and this, remember, is largely services these days). Thus, the limiting factors are the number of people, and how much value each person produces (known as productivity). Productivity has been increasing for at least 200 years. You don't need more resources to increase productivity necessarily - you need cleverer ways of doing things. We've been finding those for 200 years, and Uber's a clear example of this. Indeed, getting more out of less is the very definition of productivity.
Those resources you're worried about are not leaving the planet. They're still here. We're using up the energy, sure, but we already have replacements for that.
Take a look at the second graph on this page (http://wilcoxen.maxwell.insightworks.com/pages/804.html) which shows energy intensity (i.e. the amount of energy used per unit of GDP) in good 'ol gaz-guzzling 'merica as an example of how more output can be got from fewer resources.
That's not to say there won't eventually be a limit - there might be - but I confidently predict the limit will be our ingenuity, not natural resources. Or, to put it another way, the limiting resource will be humans.
This is not an anti-green message, just the way things are. There are other perfectly good arguments for looking after our planet and avoiding waste.