I would not recommend this method at all because this is the most risky. Although some casinos may let you deposit and withdraw without KYC but they will never let you withdraw unless or until you wager the whole balance. So now you have to first gamble the money, and you can lose everything in the process.
If you want to do this centralized way, better use the non kyc exchanges to send the bitcoin and withdraw in chucks in different btc addresses. Although a less effective method as compared to the methods listed in OP but still at least does not have a risk of losing money like in a casino.
When we're talk about privacy matter, we must avoid centralization as much as possible. What's the point of using a centralized site when you're having an option to choose the other way?
Not sure what's site you refer about centralized no KYC exchange, but my thought is Binance when they were still allow maximum of 2 BTC withdraw without KYC. Remember Binance has a KYC mandatory rule and able to freeze your coins.
Either centralized casino or centralized exchange, both of them are bad choice for privacy.