Well, Polymarket is a protocol running on ETH as far as I understand. UMA is the oracle, also run on ETH. So all the bets are custodied "in a smart contract" and paid out according to a resolution that depends on UMA which in theory is distributed. It's actually pretty cool but all the liquidity is dominated by the company that came up with it and that company being in the US, won't take US customers or facilitate bets controversial in the US through the UI they control but you could build a different UI tapping into polymarket's liquidity and their UMA oracles.

But I guess it's not exactly like that and the company probably has retained the keys to the kingdom. Also I don't know how they prevent on-chain fees. Also I never traded on polymarket because I don't want to touch shitcoins and neither am I inclined to tie my funds up in bets but I love the predictions these markets generate. For that latter part I have high hopes we will see a prediction market built on sound money that is censorship resistant open, so clients can join a global liquidity pool.