In essence, yes.
There might be a bit of poetic licence in the foreword to his short stories - I wouldn't be surprised if he somewhat exaggerated the description of events for dramatic effect - but the bare bones of the story, about coyotes attacking his dog, does seem to be true. At least, he posted about it on Twitter at the time and everyone seemed to take it completely seriously.
Frost survived a coyote attack Saturday PM. Broke a tooth on the coyote. Came out with battle scars. #GoodDog
-- 18 March 2014
Coyotes just tried for Frost again. At least three of them, one of them a pup. Parents probably teaching pups to hunt. He's okay.
-- 8 August 2014
See also the other tweets sent in response, and his responses to those. In both threads, other people raise the possibility of him using a gun against the coyotes to defend his dog, and he says that wouldn't be legal inside city limits, but he did yell at the coyotes to try to scare them away, and he was close to his dog when the attacks happened. So although the passage about him going out with a loaded gun probably isn't true, the whole thing certainly seems to be a serious issue rather than something he just made up for a story.