'should' has nothing to do with it. It provably doesn't. Even in the absence of any complicating factors or considerations of value or merit.
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The CLT simply says that the distribution of a sum of random variables will be Gaussian (as the number of random variables being summed tends to infinity).
It is not obvious to me that the agent-level difference equations in this simulation would naturally lead to the overall distribution of wealth being a sum of random variables.
However, I think you are correct and I am wrong about the population level distribution; I wrote and ran the simulation myself and got a Gaussian-looking distribution at the population level.
Do some reading on geometric vs additive means, and on the log-normal distribution for finance.
CLT dominates only if you do the sim wrong by making unrealistic simplifying assumptions (e.g. that each round is independent and variance is constant) that effectively eliminate the main parts of the simulated system and ensure that the simulation gets misleading results.