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.
This is right and just like the exchanges, they have ways of retrieving it. Before it was for free but if they have a policy of returning or retrieving it that it's paid, users have to deal with that.
But it's best to always check the networks where we're depositing because it's a headache to recover that if they say that they don't do recoveries of it.
The money will be on them and they have the private keys of those wallets so, it goes to their pockets and retrievables.