Alice and Bob start with the same $8,200. On each trade a fair coin decides who pays whom, and the amount is a random share of what the poorer of the two has, because nobody can pay more than they have. (Trades here are up to 10% of the poorer balance, a little larger than in the main simulation, so you can watch it in seconds.)
The coin is fair, so on average neither of them gains. But the stakes are set by the poorer person: whoever is behind risks a large share of what they have on every flip, while the richer one risks only a sliver of theirs.
Betting a share of what you have is a losing game even at fair odds. Lose 20% and then win 20% and you are left with 96%, not 100%. The poorer person is always playing that game with their whole stake, so a lucky streak for either of them hardens into a lasting gap, and the gap feeds on itself as the poorer person's stakes shrink with them.
With two hundred people the same arithmetic plays out between every pair. That is why wealth collects at the top without anyone cheating, and why a dividend funded by a small tax on every trade is enough to hold it in check.