No, it doesn't. The obvious cause of the huge economic growth over the past 150 years, which is what the author focuses on, is population growth. World population is expected to level off in this century.
The author also assumes, incorrectly, that GDP--money spent on goods and services--is the right measure of overall wealth. It's not. The author even discusses "decoupling", the fact that many types of wealth require little or no physical resources to produce, but fails to realize that the long term outcome of this will not be to raise monetary GDP more and more, but to make monetary GDP less and less of an accurate measure of wealth production.
Finally, the author misunderstands basic economics when he says (p. 25): "A limited life-essential resource will always carry a moderately high value." This is a common misconception. An obvious counterexample is air: air is a limited resource (Earth's atmosphere contains only a finite quantity of it), it is life-essential, but it is free. Why? Because it costs nothing to produce. And if the cost of production of other life-essential resources, like food, were reduced, those things would also become cheaper. (In fact, that has already happened to a large extent in the developed world: over the past 150 years, the fraction of people involved in food production has dropped from about 19 in 20 to about 1 in 20. The main reason food is not much cheaper as a result of this is political: governments artificially manipulate the markets for food, for example by paying farmers not to grow certain crops. This is fixable without any increase at all in our expenditure of physical resources.)
