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.
However, some casinos have their terms on this kind of transaction and their stand usually is that they won't give the time to return it to the user. Though they have the control, unfortunately, most sites won't entertain such request from the user who mistakenly made the transaction. So this is another free income for the casino.
For players, make sure that before you hit the send button, double-check or triple-check the addresses and the network that you are sending it to. Because most transactions are irreversible. It would be like a doing a good act if the casino will return the coins to the user who made such mistake. Because not many will do such reversion of funds.