The bag pictured on page 16 appears to be what I call a shooting bag, or hunting bag. Others might call it a Possibles bag. I do not think it is a bag for carrying game. The weave is unique.
A simple haversack would serve for carrying small game, or perhaps an open weave bag of some sort and of similar size to a haversack might have been used by the town dandy or gentleman farmer. Or just a old feed sack could be used.
I have seen fancy shooting bags with attached leather straps with metal rings hanging down from them. The strap is pulled through the ring, the critter's foot is inserted in the loop, and it is then drawn tight, letting the animal or bird dangle securly attached to the bag.
However, it is easy to just tie a critter's feet together and hang it over your belt.
Of course you would get blood all over your leg if you did that. As a kid, many were the times when my Mother would yell at me for bloodying up my bluejeans that way.