[thaumasiotes]

Even without the bimodality, you wouldn't expect a normal distribution of ratings.

1. Assume that chess ability is normally distributed in the population.

2. Assume that people who are terrible at chess are more likely to stop playing chess than people who are successful.

Then you've sampled the underlying normal distribution mostly from the top end, and that new, highly skewed distribution is what you'll see when you measure everyone's rating.