As I understand, a print publication can't have a business entity in the US if it's owned by a foreign adversary. Given that, an American could still travel to the foreign country themselves and bring an issue back. That would be similar to side loading apps.

In order to comply with the law, Apple and Google cannot distribute the app because it is deemed to be unlawfully owned by a foreign adversary; that's the ban. But anyone who wants to get it through other means can still do so. Presuming that's how it works, it doesn't seem to be logically different from radio/print media.