I am not sure where you are hearing this from? Do you own any games? I can tell you from personal experience and from talking with lots of Gamefowl owners, that they are some of if not the best birds out there. Not a man fighting bone in their body.
OEGB are not close to games. When OEGB were created they just used regular bantams, no game blood ever went into them. Real games are great with people and *bad* with other roosters and birds of prey.
Not fighting people, just other males. They are great with people even small kids. And they will fight of most predator's better then regular roosters. And they are drop dead gorgeous.