gamblers, where do the coins actually goes to in reality?
Are coin send with wrong network actually lost?
Do casino have a system that can retrieve the money?
The coin sent to the gambling site address on another network is not lost, the gambling site has the private key that can be used to access the coin.
ERC20 and BRC20 generated on the same wallet will have the same wallet addresses. So the coin is with the casino and they have access to it.
You have given clarity to the question and have answered it, so far the coin sent was to a gambling site it is not lost and the gambling site surely has access to it. They can decide to withhold it if such a mistake is against their policy which should be clearly stated in their TOS. If that is the case I guess there's nothing the gambler that made the wrong deposit can do, he will have to see it as lost coins. But I think that it is not fair on the side of a casino to withhold the coins, they should know that it was a mistake and reconcile the funds so that the gambler can have access to it.