No, it's not. A tortfeasor has to be a person. Dogs are not legally persons, so they can't be tortfeasors.
> while the owner is responsible
Yes, exactly--just as any other tortfeasor is responsible.
> there's some simplicity in saying that the dog broke the rule of the road that lead to the accident.
You could say the dog "broke" the rule in the sense that it moved its body in a way that the rule prohibits; and in a mundane description of the facts of the accident, yes, that's what you would do. But the dog is incapable of understanding the rule in the first place, so the owner is responsible for training it appropriately (or, as I would imagine is much more common these days, keeping it on a leash and exercising reasonable prudence in controlling the dog).
I think it's debatable whether calling the dog or the owner the tortfeasor makes more sense when the dog is loose, because while the owner is responsible, there's some simplicity in saying that the dog broke the rule of the road that lead to the accident.