> Why is "if you gambled but we found out you weren't allowed to gamble, we'll take back your winnings but not give back your losses" legal?

I don't know the actual law is, but it could be that the customer is the one who committed the crime of illegal gambling. If that's the case, it doesn't matter if keeping his winnings is legal or illegal, if the gambler brings suit he puts himself in legal jeopardy and I don't think the courts will enforce contracts associated with illegal activities (e.g. a hitman can't go to court to force his client to pay).