Referring to wild animals as "game"

Solution 1:

Think of the word game, meaning something with rules done primarily for fun or to pass the time - that also applies to the ritualized hunting practices of the medieval upper classes. Game animals and game birds are ones that were hunted for sport - deer, elk, pheasant, quail, and a variety of other fowl - and then eaten (even though foxes and other animals are also traditionally hunted for sport, as they are not eaten they are not game).

As the European upper classes began colonizing the rest of the world, they began hunting new and unique animals, terming them big game (lions, elephants, rhinoceroses, etc), even though the meat was not always eaten afterward.

In the contexts like naturist writings, wilderness fiction or explorers' monogrphas, game alone usually refers to an animal of the deer family, or the meat thereof.

Solution 2:

It does indeed come from the fact hunting animals is a game or sport.

From the Middle English 'gamen' which meant sport.

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