Most of the time, it's just to try and delay the withdrawal.
Sounds convincing. The big question is, why would these gambling or casino websites ask KYC only if a player win big amount of money, why they didnt ask KYC before a player can proceed to play in their website. Im thinking there will be another reason for that aside from just delaying the withdrawal.
With large withdrawals, KYC verification is required. Some bookmakers want to verify the identity of the owner and complete some legal requirements when the government agency checks large transaction amounts. Also, verify to avoid money laundering of some black credit institutions.