I was watching Futurama and there was a scene where Fry tasted a steak and said it tasted gamy (or gamey). Now I've looked up on several dictionaries and they all state that in the context of meat it describes a strong flavor or odor of game. However when I lookup the aforementioned word game and it's plethora of definitions there isn't a single definition that relates to any form of meat or even food for that matter. What does this game exactly mean?
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This probably goes without saying, but it hasn't been directly addressed by any of the existing answers.
The word game, which originally and primarily means roughly a form of amusement, evolved to mean meat by way of hunting as a form of amusement.
OED definition 15 walks the line between the original meaning and the meaning referring to hunted meat.
15. Originally: †entertainment derived from the chase (obs.). In later use: the sport of hunting and shooting (or otherwise catching or killing) animals, birds, etc., as a countryside pursuit.
From there it took on the meaning referred to here, which developed the adjectival form gamey.
The flesh of a game animal or game bird used as food.
This form is first attested in 1658.
Game in this context means:
a. Wild animals hunted for food or sport.
b. The flesh of these animals, eaten as food.
Source https://www.thefreedictionary.com/game (Look at the #9 definition)