A lot of comments here are conflating the notions of "property ownership gives individuals a stake in the system" and property requirements for voting. They're not nearly the same thing.
To understand the point of the author you need to look back, deeply back, at the history of human society. For most of human history, most people did not own any property. In a feudal society, for example, a few lords owned everything, and everyone else worked for them and owned nothing.
The "American experiment" was radical in that it placed the individual at the center of governance. The U.S. system of government is "built up" from citizen consent, not "pushed down" from a divinely-granted right of hereditary rule.
In order for this system to work, citizens must own property. Otherwise, they don't have the resources to collectively enact change. The Bill of Rights presumes citizens who have the resources to speak, associate, petition, etc. That's why it is worded to constrain the government's power, not worded to grants things to citizens.
The fundamental idea behind American democracy is that Americans have the means to pursue their goals and to influence each other.
This is why it was so much easier for early U.S. citizens to found churches and corporations than it was in Europe. European churches and corporations were top-down, and therefore few and conservative. U.S. organizations were bottom-up, and therefore many, diverse, and innovative.
So... that's why property ownership is at the heart of American democracy.
But what about:
> deliberate and intentional effort has been made to ensure that only people who own a lot of property have any voice in the system
There's actually a lot of evidence against this, for example the entire labor and environmental movements. Collective citizen action has worked a lot of change to the U.S. over the years, and I predict it will continue to do so.
All that said, I think it's a pretty far reach to claim that the American experiment is at risk because a few people don't want to buy CD's or cars anymore. People still like money and things! The real estate market is not drying up. There's plenty of property being owned and desired by Americans.
I think that lack of money is a bigger issue. Over 40 million people in the U.S. live below the poverty line! I think that's a much bigger problem for American "stake in the game" than whether someone who has disposable income decides to spend it on a Kindle instead of books.