"Gamey" flavor just refers to the wild taste that game, like deer has. It is a stronger, tangy, earthy flavor that the others are right, is very difficult to describe if you haven't tasted it.
Although wild game is lower in fat than grocery store meat, that doesn't make it taste gamey. Also, although wild game tends to be tougher, because the animals get more exercise, that doesn't make it taste gamey either.
Gamey flavor comes from the fact that the animals in the wild eat a very varied diet of weeds, acorns, wood bark, etc. This flavors the meat in much the same way that peanut fed hogs in Virginia make their hams taste distinctively. Since we are used to eating meat that is grain fed, which has a much milder flavor, gamey meat tastes strange to us now, and most people don't like it.