gamebag

[geym-bag]

noun

a bag, usually of leather or canvas, for carrying game, especially birds, killed by a hunter.

Origin of gamebag

First recorded in 1820–30; game¹ + bag

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

The eagle, luckily unhurt, was rewarded with a small pigeon from my gamebag.
The Swiss Family Robinson
Jean Rudolph Wyss
"We sure will," answered Todd, and he gave each of the party something to carry on his back and in his gamebag.
Dave Porter at Star Ranch
Edward Stratemeyer