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.