Actually i think it has some risk. Because Some gambling site are not enough careful about our information. But some companies are careful. Overall we have nothing to do about it because some companies tarms and conditions are KYC. It has some positive side and has some negative side. On the other hand for Bitcoin transaction has no mandatory KYC because It's transaction held Through Blockchain. But gambling site needs KYC to avoid scam. So i Think gambling company did it for safe from scammer.
Do you mean all centralized sites that aren't gambling are safe? there's no difference if the site is gambling, exchange, robot trading etc, all of them carry a same risk. This is not about Bitcoin, off topic if you discuss about Bitcoin transaction. You can gamble with fiat or online money on an online casino.
KYC can be used to avoid scam, avoid abusers, complying the regulation etc.