We no longer have a predominantly-competitive economy. Cartels and trusts are the norm in the "new" America, and they own nearly half of the political system. Competition has become a command toward working people who are expected to compete to see who is most willing to suffer for economic elites. What we get from the non-competitive economy is suspect.
The terms you're searching for are "oligopoly" and "monopolistic competition". While I'm highly skeptical of oligopoly, I don't see it as the cause for the recent abuse of the American middle class. Instead, we are all laboring under the yoke of inefficient taxation and benefit price inflation caused by reckless demand subsidies.
Thiel is nuts, but I don't think he's arguing that monopoly breeds innovation, rather innovation breeds monopoly and monopoly pricing leverage. "By "monopoly," I mean the kind of company that is so good at what it does that no other firm can offer a close substitute. "
The sheer idiocy begins when he starts ranting about America's misplaced faith in business competition. Competition is what spawns pricing leverage, and inefficient duplication of processes by competing interests is what keeps us employed and constantly innovating.