Seeing that there's no blood at all and the puppy in question appears very well groomed despite the hook sticking out of its face and the assumption it was just stuck in the ocean to attract sharks or about to be? Yeah, that particular image is probably a shop.
Furthermore, it saddens me that nobody is up in arms about fishing for sharks and gators in the first place -- most species of sharks, ESPECIALLY ones big enough to take a live dog as effective bait, are very much endangered, and while alligators are in some locales invasive pests, in others they are similarly threatened.
Also, the penalty that the petition asks for is significantly harsher than the penalty for rape in many, if not most jurisdictions.
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But this is Dwarf Fortress. We're a land that frequently raises "pet" animals like normal people raise pigs. While our little alcoholics wouldn't think of hurting personal pets, unlike humans they see no attachment to stray members of the same species, and furthermore without the technology to spay or neuter Fluffy we find ourselves suffering dire problems from the overpopulation of domestic animals.
So, in the context of DF, I'll use puppies and kittens to lure goblins and their ilk into giant meat grinders. If I take an ocean embark and can manage the engineering to do so, I'll use them as "Bait" to capture sharks, salties, and maybe even a giant sperm whale for my aquarium -- though as that mechanism is seldom lethal many more such animals will still go to the butcher's shop to fuel my food industry, my bone bolt production, my leather clothing industry, and the skull totem trade.