There the notion that American politics often resembles poker while the Chinese rather play go.

I think there is a reasonable case that go teaches certain useful skills beyond 'just' providing generic brain excersize. You have to know which groups to fight for and which to abandon, you have to prioritise, you have to avoid becoming fixated on any one part of the board. 'Play urgent moves before big moves' is good life advice.

Diplomacy might train people to avoid being stabbed in the back, or it might train them to stab other people. You could even invent your own, positive-sum game if this seems like a potential problem.

The whole situation also raises a bunch of stress in applicants which can cloud the body language.

Politicians are going to need to make decisions under stress, and deal with stressed people.

Are you aware of any company for which hiring people with high social skills is important who let's their applicants play diplomacy?

Since what I am proposing is similar to a job application process, looking at the hiring process for high-paid corporate roles could be a good starting place for anyone who was actually trying to implement this in real life, as opposed to my attempt here to paint a rough picture of what the process might vaguely look like.

I do know that some financial companies have 'the theory of poker' as required reading, and a quick search turned up this recent idea of using custom video games but I think in general companies use interviews more.

Of course, using interviews to select politicians simply allows the government to form an aristocracy. Companies are at least accountable to their stockholders. The idea of turning the government into a company and giving the people shares was, I believe, an idea of Moldburgs'. I find it more interesting than reverting to monarchy, but it has its downsides, especially that, given the distrust of the financial system, I cannot see it having to popular support to get started in the first place.