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.