OK first I don't know the laws in your state as far as cock fighting, but if it's against the law and you face off 2 roos you can be in trouble. Just a warning, not a lecture.
I think taking a chance with your Hatch being killed isn't the way to go either.
Your neighbor owns a territorial bird and lets it wander like some people do dogs. If it attacks your livestock, usually the same laws apply. If it attacks you family, that is still a legal matter. If there are small children around, they can be seriously hurt and then he's looking at a law suit.
You need to make a report with Animal Control. If there are injuries, the police. If you otherwise get along with the neighbor, do your best to explain how his Stag is affecting your families ability to feel safe on their own property. If he doesn't care, start reporting him.
There are several Game roos who are loose in my neighborhood. Most people around me own them and they usually own several roos at a time, but keep them penned up separately. If one ever attacks one of my birds or my family, it will be soup.