Murder, by definition is the killing of humans (actually, homicide is). Not dogs and not cats. Dogs and cats are not people and considering them "part of the family" doesn't make them so.
As for the story, it sounds like a failed SSS (shovel, shovel, shut up in this case). If you're going to SSS, they better stick with it. Without bodies or a video or really credible witness, the only thing they can get you with is tricking a confession out of you.
Yes, murder concerns people. Good point.
In the article, the woman whose dogs were killed said she wants to change the law. How would that work? You see dogs killing your livestock and all you can do is make loud noises to try to scare the dogs away. Crazy.
If you hit the dog with something like a shovel, you might kill the dog. Then the owner of the livestock, under the proposed law, would get jail time for protecting livestock. I don't think this law will fly. California has a lot of agricultural land and a lot of livestock, and I am sure people want to protect that livestock.
I like dogs, but people have a right to defend their livestock. I don't see how the law can work otherwise.