KYC was not a thing a long time ago but unfortunately, things have changed now though I guess small time users can still transact with smaller amounts. As long as they don't exceed on the limit given to them by the exchange, they won't be asked to do a KYC. I hope this rule can also be applied on the gambling sites.
But do you trust exchange with your funds? I don't think we should hand our funds to any exchange if we have in mind not trading but for KYC also being a small gambler don't ask for too much documents and you can easily verify yourself to withdraw the funds but for big withdrawal it's problem as level of KYC goes up.