A .22 handgun makes alot of sense especially when your longarm is something else like a high powered rifle or shotgun.
You might spend all day glassing for big game and come up dry yet on the hike out you'll spot or spook all sorts of small game.
My dad once took a ruffed grouse with a 30-06 shot to the head. He used what he had. In a survival situation it is small game that will feed you in between the occasional big game kill, if you get a shot at something large at all.
By using passive food gathering means, trotline, traps, snares etc. You can go about doing active things like improving your shelter, foraging, collecting firewood etc. There's so much stuff you have to get done in a day that you have to "multi-task" as much as possible. A .22 handgun turns these other "hands-on" activities into hunting trips as well. Mac