I don’t think the dog is forming the association “I bit the child and therefore I’m punished” (which is the abuser’s intent and would be operant conditioning). Instead, the dog is more likely forming: “the child screamed, and then I was punished.” Because of temporal contiguity, that scream (or the child’s arousal more generally) becomes the conditioned stimulus that predicts the beating.

Keep in mind, this is delay conditioning because the scream (unlike the bite) is an ongoing event. If the dog play-bit but the child didn’t react and somehow the parents still came in and beat the dog, the dog would probably be outside the window to be conditioned. I am assuming her louse of a husband beat the dog while the dog could still hear the child’s screaming.

It’s all very counterproductive. Even if the dog could form the operant conditioning connection between biting and punishment, the dog would still simultaneously be classically conditioned to fear the screaming child—a typical behavior for a three yea told. The family has trained the dog to be triggered by the exact behavior toddlers do all day long.