Does anyone know what the rules/law is surrounding this situation? How can I ensure I get the domain I purchased?
If they notified you of the error, refunded your money then most likely there's nothing you can do. The sale wasn't completed if you never took ownership of the domain. You have no actual loss you just didn't get what you wanted.
If you happen to be able to show that they backed out of the deal because they gained knowledge of what your intended use was then perhaps you have standing, but that's still unlikely.