My colleagues are also right, and what term you use depends on the register of your translation. Look in any poultry hatchery catalog online (such as Murray McMurray) that specializes in old or exotic breeds of poultry, or any poultry breed or show site, and they use the term game cocks, and there are many breeds, such as Old English Game, Birchen Game, Red Pyle Game, etc, etc, and these names refer mainly to the plumage pattern. In fact Cornish Game hens refers to the fact that one of the ancestors of this breed (which is nothing more than an ordinary broiler chicken slaughtered at a young age!) was the White Cornish Game...which, when crossed with the White Plymouth Rock breed, produces the hybrid broiler chickens, which is what most of the chickens you buy in the super market in the USA are. Game in this sense, when applied to chickens, refers to cock fighting,i.e., gambling, fighting, or contests, not game in the sense of wild birds or animals to hunt. And it's perfectly legal to raise and breed these birds in the USA; they are beautiful and always eye-catching at shows, it's just the actual cock fighting part that's illegal.