Like many others have said, the coins aren't lost. They are held by the casino since it's a centralized platform, they own access to the keys. Honestly from the quoted part of the op, it's obvious that the sender in this case was careless. You can't possibly make same mistake twice and brag about it. He's first mistake was taken slightly by the casino and they might have gone through some unusual processes just to refund his account. But he decided to repeat same mistakes again. At least he could have learnt from he's last and try to be careful when sending the next.
On the other hand, the casino should at least consider he's request if they want to keep there reputation of their services.