I hunt quite a bit... in fact I need to go kill a bunch of deer over the next few months (25+/-).
...and although I have killed many with a .22LR or .22 Magnum... I have never considered it a "Big Game" chambering I would list regarding "83 elk, 128 deer, 78 pronghorn, mountain goat, oryx, muskox, dall, desert, and bighorn sheep, black bears, mountain lions, moose."