I was conjecturing that the distribution would be closer to Pareto for everyone (including people who've never learned how to play chess), hence why I said that "active players" is a big caveat.

> increasing populations make things look more Gaussian - in all natural circumstances.

This is just not the case, there's plenty of "natural circumstances" where populations have non-Gaussian distributions.

Perhaps you meant a specific type of population, like chess ratings? I'd be interested in seeing what you find there, but all I've found shows significantly distorted tails (not to mention a skew from 1500).