KYC is very important for the security of a user's money or any transaction. If you ever win a big amount in gambling then you are requested to do KYC. Because they want to be sure through KYC that you are the real person. It is better to do KYC in the casino because you do not have to face any problem in case of large transactions.
If they want to check and know that you're the real person or not a kid then they should ask KYC upon registration or upon deposit just like @Maslate have said. KYC may sounds secure though but they should try to be more reasonable and not just ask these questions if we're trying to withdraw our winnings. Although I'm not against KYC as long as that specific casino is reputable and trusted but I'm just curious on their procedure.
Well, I don't think there's anything to be curious about because crypto exchanges do this same thing, there are several exchanges that allow you to deposit, trade and withdraw small amount of money, anything you are ready to deposit, trade or withdraw a large sum of money, you will be asked to upgrade your account from level to level 2 or 3, depending on their tier system, and we all know that this tiers are nothing other than different levels of kyc, there are even other exchanges that allow you to deposit huge sums of money without kyc, but upon trying to withdraw, you will be asked to pass kyc verification before you can withdraw.
It's nothing different from what casinos does, casinos are even better since money you are trying to withdraw is money you won, for some exchanges like I said before, you will deposit your hard earned money without passing kyc but you will be required to pass kyc before you can be allowed to withdraw same money.