When it’s Monopoly money for predatory games, and the retailer hasn’t lost anything by giving a refund? Yes.
But this class of problem is broader in scope - there are all kinds of services and products kids might be using their parents' cards without permission, and in a lot of cases there might be no real material loss to the company if they "eat" the refund. I think it's going to be very hard to sensibly adjudicate anything broad specifying when it's OK for the retailer just to eat the loss and when not. I don't think it's reasonable to simply declare that "your kid used your credit card without permission" is the same class of problem as "your credit card was stolen."
Perhaps the best thing to do is have a mandatory refund policy on electronic products and services within say, 120 days, but this won't be very popular, and while I'd support it, opponents would likely rightly complain that a lot of consumers would abuse it.
I do disagree with your "this is a different situation" though.
In both an entity (unknown person/child) accessed your card details, and used it for a purchase without your authorization. Theft by any other name (aka "unauthorized charges") is still theft. It's just your child doing it in this case.
If, for example, you give your card to a bar and they charge your your bill, then charge someone else's bill to your card because they skipped on their bill, it's still theft even though it would be called an "unauthorized charge" in the banks eyes.
Besides, a lot of this is why there's processing fees (2.9% + $0.30 for stripe for example), chargeback fees ($25 instantly if someone issues a chargeback and more if you escalate after losing once), and interest on CC products. Even if the bank can't get their money back from the company, they will likely still make more on you by giving you that refund than not.