There's nothing to worry about if you are just playing with low balances only since for sure the casino owners will not require you to present your KYC documentation. The only thing asked for that matters is the one suspected launders money that's why they got notification to do the KYC to verify how legitimate their transaction is. I'm also sure that government doesn't mean that all players are criminal but they are only pointing those people who do so.
If the amount does matter when it comes to enforcing KYC then people will not be crying out for hundreds of bucks on the scam accusation, KYC can be asked for different reasons and when it small amount it maybe due to accusations of multiple accounts which is against ToS of most of the gambling sites due to promotions and contests.