I believe they were hunting rats. No creatures no matter how humble or seemingly unworthy of sport are safe from Charles Musgrove's gun. Remember his crawling around in the hedge on the walk to Winthrop looking for weasels?

I assume that the rats would be hunted since they are pests, not because they edible or prize trophies. Growing up in North Dakota, staying on my friend's farm for the summer we were always sent out to the farm yard to hung gophers, since they dug up the place and caused livestock injuries with their burrows and were generally a nuisance. It's not the most dignified hunting pursuit, but it is kind of fun in a totally mindless, destructive sort of way. The sort of thing that 12 year old boys adore. (And 12 year old tom boys, of course!)

I always find it kind of charming that Charles is so boyishly passionate about rat hunting. And yes, one can imagine Benwick getting sucked in, perhaps unwillingly at first, and then just giving himself over to it--the way one finds oneself playing a moronic video game hours after one was just going to make one little attempt at it. I think it's funny that Charles doesn't recognize his bravery until he is rat hunting with him. What could be the dangers of chasing poor creatures around the barn in comparison to the Naopleonic wars!