Uh, actually, I think he is talking about eliminating your rivals, which used to be fairly illegal but now is less so, for reasons nobody seems to talk about much. According to the transcript, Thiel said:

Generally speaking, capitalism and competition are better seen as antonyms than as synonyms. To compete isn’t what you should set out to do. That doesn’t mean you should slack off. To succeed you probably need to work intensely. But you should work on something that others aren’t doing. That is, focus on an area that’s not zero-sum. 

Sometimes, though, you need to compete. Monopoly is the theoretical ideal that you should always pursue.

That's just Econ 101. As an example of a perfect competitor, economists always used the example of a wheat farmer, which always struck me as pretty grim. Inventing a monopoly is a lot more fun, but the real money is in holding on to the monopoly.

Thirty-years ago, I went to work for a 2-year-old firm that was the first in the world to figure out how to use supermarket checkout scanner data effectively for market research. After five years of very hard work, there were three firms in the industry, tearing each other to pieces in a price war. My boss merged our company with the richer of the two competitors for a very nice price. The Reagan Administration shot down the merger on antitrust grounds because clients like P&G complained that the two remaining firms would make higher profits by not cutting prices as fast.

That seems so 20th Century by now.

The implications of all this for, say, immigration policy are obvious, but nobody gets them.

Thiel has some good nerds v. jocks thinking:

In thinking about building good company culture, it may be helpful to dichotomize two extreme personality types: nerds and athletes. Engineers and STEM people tend to be highly intelligent, good at problem solving, and naturally non zero-sum. 

Athletes tend to be highly motivated fighters; you only win if the other guy loses. Sports can be seen as classically competitive, antagonistic, zero-sum training. 

Sometimes, with martial arts and such, the sport is literally fighting. 

Even assuming everyone is technically competent, the problem with company made up of nothing but athletes is that it will be biased towards competing. Athletes like competition because, historically, they’ve been good at it. So they’ll identify areas where there is tons of competition and jump into the fray. 

The problem with company made up of nothing but nerds is that it will ignore the fact that there may be situations where you have to fight. So when those situations arise, the nerds will be crushed by their own naiveté. 

So you have to strike the right balance between nerds and athletes.

Back in the 1990s, I pointed out that nerds v. jocks is a useful framework.

In the same lecture, another Paypal founder offers some insights into diversity:

Max Levchin:  The notion that diversity in an early team is important or good is completely wrong. You should try to make the early team as non-diverse as possible. There are a few reasons for this. The most salient is that, as a startup, you’re underfunded and undermanned. It’s a big disadvantage; not only are you probably getting into trouble, but you don’t even know what trouble that may be. Speed is your only weapon. All you have is speed.  

So how do you move fast? If you’re alone, you just work really hard and hope it’s enough. Since it often isn’t, people form teams. But in a team, an n-squared communications problem emerges. In a five-person team, there are something like 25 pairwise relationships to manage and communications to maintain. The more diverse the early group, the harder it is for people to find common ground. 

The early PayPal team was four people from the University of Illinois and two from Stanford. There was the obligatory Russian Jew, an Asian kid, and a bunch of white guys. None of that mattered. What mattered was that they were not diverse in any important way. Quite the contrary: They were all nerds. They went to good schools. (The Illinois guys had done the exact same CS curriculum.) They read sci-fi. And they knew how to build stuff. Interesting to note is that they did not know how to build stuff the right way. It turned out that scaling up would be very challenging for PayPal because the 26 year-olds who were managing hundreds of thousands of credit cards didn’t make all the optimal choices from the beginning. But there was great clarity in the early communications. There was no debate on how to build that first database. And that alone made it possible to build it.