coyota1, you're worrying too much about labels. I've shot running critters with a light sporter .223, a lighter-weight .243 carbine, and a full-size '06. I figure that "game animal" includes coyotes if I'm hunting coyotes.
OK I see. Where I live if a coyote is on the run, it's gone, and so are bambi most if the time. Lots of heavy forest and swamp here.