I do understand the Law yow, and he is violating the law.
They do have a way of knowing he's making money by opening his livestream, they dont need him to show bank statements or to remit money to Japan to enforce the law, they can take action based off reasonable suspcion.
Conducting such an investigation on a tourist that might leave after a week is obviously a waste of money and resources, but they might do it anyway as a warning to other livestreamer degenerates, or they might refuse him entry the next time he comes to Japan if he's already known to Immigration