Game chickens should never be, and generally are not, aggressive to people. Game birds are usually the tamest, most trustworthy fowl you could ever have around because the breeders of such have had a policy of ruthless culling of all man aggressive birds. Think of the problems a manfighting gamefowl could cause, it simply has never been tolerated. The nastiest chickens are typically the commercial egg strains, as no one gives any attention to their temperament at all. Gameness and aggression are 2 different things, and so is fighting humans vs other male fowl.
Now, as to their attitude towards other fowl, a game chicken will not tolerate other males, PERIOD. It has nothing to do with how they are raised, it is innate, genetic, part of their make up. You won't undo thousands of years of selection by raising them any particular way. If they do tolerate other males, they are not "game". If you want this type of chicken but not the challenges in raising them, I'd suggest Cubalayas, Sumatras, Dutch Bantams, etc.