The logic behind it, I think game theory, is simple and does not just apply to democracy but any system of corporate or state government.

It goes like this:

Suppose there exist 2 parties to a conflict of interest. I want Z, but you also want Z, and this is a rival good, only one of us can have it at one time.

Then it is possible for 1 party to play ball with the other party, but IFF there is a different, separate conflict of interest where the trade can be reversed.

So I win A, but only if I allow you to win B. 'the next time'

This logic only can work if we allow each other to be winners.

Suppose our economic incentive was to 'defect' in game theory parlance, and defect always. Why would this be so?

Perhaps because we're in a zero sum game instead of a positive sum game. Perhaps I must win or I will die, in which case my non-cooperation with you is non-negotiable.

"I want Z, but you also want Z, and this is a rival good, only one of us can have it at one time."

sama, and Thiel, believe technology solves this by turning a potential rival good into non-rival goods. Or put more simply; if everybody can have stuff they are happy.

There can be exceptions to this logic, like a mother choosing her child's survival over her own in a pregnancy gone wrong. But in a world without growth, without those potential negotiations 'violence' becomes selected for.

The important realization is not the trivial 'more stuff makes people happy'. It does, but the real reason why growth is a big deal is that in the long run it selects for outcomes which don't lead to deadlock leading to violence.

Where I part company with Sam, is the belief that democracy is worth saving. It is worth saving representation, each entity's self interest in a system must be recognized yes, but not democracy. Ironically equal voting must lead to unequal outcomes. Right from the initial premise it does not hold up against physical reality. Like genetics, circumstance, and all of history. There are other systems in G-space that have the potential to be much better at governing. That includes systems in which people would feel much more represented than they do in our current system. Equality of votes is like a sledgehammer instead of a scalpel. I mean even the NSDAP had policies on the environment and health most people agree with in the present. What does that say about our ability to select?

tldr; The relationship is close to axiomatic in game theory and democracy when looked at in the cold light of day is a pretty dim worldview to start with.