When one describes the taste as gamey, they are indicating that the meat has a tart taste. It isn't the most pleasant taste. This taste is noticed more in the fat of the meat. There are many reasons why something would taste gamey. One is not allowing the meat to cool long enough. Another is based on the animal's diet.
The animals that generally eat a wild diet; their taste will be more gamey. There are ways to lessen this taste when preparing the food. One way is to clean the meat thoroughly and remove the hair, fat, and skin. Another way is to season the meat.
The feeding patterns are responsible for the gamey taste of the meat. "Gamey" meat is stronger and has a more distinct flavor. Gamey meat is associated with almost all livestock. Livestock with gamey meat feed on wild grass and wild food. Domesticated livestock is fed hay and other dried food and the meat has a milder and even taste.
Gamey taste is due to abnormal diet patterns. Gamey-meat livestock eats whatever they want and also eat a non-regulated diet. The versatility in their eating habits tends to affect their flesh and accumulation of various chemicals in minute amounts which is directly responsible for the gamey taste.
The taste of "game" (venison is the stereotype) is different from the taste of "domestic" meats such as beef, pork or poultry. The expression "gamy" describes meat that tastes or smells different, perhaps stronger, than the bland, familiar tastes. "Gamy" is often extended to mutton (sheep) or lamb, goat, camel, and animals such as mountain sheep, moose or bear, that people do not ordinarily eat. Range-fed (grass-fed) beef tastes different from the meat of feed-lot cattle, and we say that the range-fed beef is "gamier."
The taste of a particular type of meat is determined by: the characteristic chemistry and type of muscle and fat, of the breed of animal (and others of its family), the animal's diet (grasses, leafy plants, flowers, fruit, bark, etc.) and nutrition (protein, minerals.) The same effect of diet is even more obvious in the milk of nursing females; and the animal's movement and activity patterns. Range fed cattle get more exercise than do animals kept in feed-lots, so the leg and rump meat of grazing cows has more myoglobin and is "gamier." This is why poultry legs, thighs, wings and backs are darker and have stronger flavor than the breasts.