I think this is extremely important. I also think that there are some myths. Different animals taste...different. A Cornish game hen doesn't taste like a chicken, and neither does a goose taste like a duck. Squirrel will NEVER taste good to me. Everybody up here loves their Friday Haddock fish fry. Hate to spoil it for you, but that mild, white, flakey meat comes from a bottom feeder. How something as delicious as northern pike can come from such a slimy, stinky, miserable animal is beyond me. I don't think you can make any broad statements about where an animal lives or what it eats and link it to flavor. There are probably many situations where one factor or another affects flavor, however. There's also the deal where some animals simply taste gamey or fishy by nature.
Closing thought: Why?
Gamey
Slimy
Skinny
Stinky
No consistency in spelling, lol.