The keys to economic growth he identifies are (1) property rights, (2) scientific rationalism, (3) capital markets, and (4) adequate transportation/communication. All of these appeared in sufficient form for prosperous growth several hundred years ago.
There is of course no guarantee of continued growth at same rate as last several hundred years. But given the conditions that have prevailed it has settled at a fairly stable rate as sort of a natural law.
Without two hundred years of unsustainable consumption of fossil fuels, property rights or capital markets wouldn't have given us a fraction of the economic growth that we got. Stock exchanges don't do much for you when 97% of your population are either subsistance peasants, or make hand-crafted tools used by subsistance peasants, and you have to spend 8 hours a day banging rocks together to stay warm and to scare away mountain lions.
#4 is also only possible because of #5.