It was hard to find. Here's where they finally state their case:
"What is anathema to Thiel in “Star Trek” is the notion, drawn from Isaac Asimov’s fiction, that the market is but a temporary solution to imbalances in supply and demand, and that technology and plenty will eventually make it obsolete"
So, he "fears" that capitalism will go away...according the them anyway. They seem to source some of that thought from what they call his "Cato Essay", here: https://www.cato-unbound.org/2009/04/13/peter-thiel/educatio...