Well, as far as I know, you can play without KYC but if they later ask you to do a mandatory one and if you refuse to do it, you only have a right to withdraw the deposited money but not the winnings.
Which is usually what happens when people complain about "casinos stealing their funds". But it is your choice in the end.
In my country there are many licensed local online casino that doesn't require KYC but you can only able to play on these casino if it's connected to online wallet app that requires KYC. Withdrawal are unlimited and no restrictions I trust these local casinos because I already tried them and its recommended by the local wallet app. The good thing is local casino here are easy to access just deposit and you are ready to gamble.
Unlike other online casino if you are going to gamble like most of the casino here in the forum KYC is mandatory.
I am hoping that someone will develop an wallet app for crypto with one time KYC that can just connect to any online casino without asking for KYC. Same as our local wallet app here in my country.
Most online crypto gambling sites have their own terms when it comes to KYC, hence, usually, you need to comply the kyc requirement on their site itself. Now, it is possible what you have suggested that you only need to connect your wallet to the site and there's no need for you to comply kyc on the site. That is, if the site will recognize the app that you are using. But for now, most online casinos are not yet connected to third party wallet app as you need to deposit directly on their site. Such route is very possible but the site should integrate that payment method in order for them not to require their player with kyc protocol.