Capitalism is a cultural phenomenon. It is deeply ingrained in the American way of life. It appeals to our sense of independence and the idea that we can accomplish anything with hard work. To a certain extent, that is a lie. We don't have pure capitalism. Independence is a myth, and we do have a strong but undiscussed class system that prevent anyone from being able to do anything.
The answer is more complex than the gist I am about to offer, but it all comes down to the sense of ownership that Western Civilization is accostumed to as opposed to the government-meddling thirld world nations who have been denied this very right. Owning homes, businesses, investing in bonds, selecting stocks and bonds are rights that come along with the constitutional rights of individuals. Yet, in developing nations everything from laws to rights to the very foundations of their nation get switched, changed, and abused by embezzling government officials.
Yet, innately, Americans (for example) would not let that fly simply because it is part of our nature to never allow outsiders to meddle with what we believe belongs to us. This is a mentality that the world takes for granted, but many people do not realize that many other countries actually fear to feel or think the way we do because they get shut down, or shut off.
It is this same attitude of self and ownership that allows our nation to invest and use up national wealth for the creation (or so we hope) of programs and services that we can also use for our own benefit. As you know, some developing countries thinks of the US as a "selfish and arrogant" country for that reason, yet, it is important to notice that our system works with our reality and circumstance, and that is basically what the book is trying to say. It works for us because we have the innate spirit to make it work.
I really do not know what Hernando De Soto say about reasons for triumph of capitalism. But if he has claimed that triumphed only in the West then he is wrong on two counts.
First, what is popularly believed to be capitalism has triumphed in Eastern Countries - Japan is a glaring example. There are other small examples like Singapore and Hong Kong. Australia is also not in the West - but you may not consider it a very successful.
Second, even where capitalism has triumphed, it is not a pure Capitalism. Even U.S.A. government engages in many welfare activities and has strict lays to control monopolies and Monopolistic behavior.