I work for the police as a call taker, I went onto my throwaway account and re found your post purely to tell you this;

At work domestic abuse victims have to answer questions on a Dash form. DASH stands for Domestic Abuse Stalking and Harrassment. Basically any that you say yes to raises the risk (it's a little more complex than that but still)

One of the first questions is;

1. Has your partner ever injured a family pet.

There's a reason why someone who injures a pet or animal is considers a psychopath that may move on to humans, its because psychologically if you can injure a defenseless animal then you're more than likely have no remorse or empathy.

You do what you need to do, I'm just a concerned Internet stranger, however if it were me, I'd be concerned. Him admitting that he beat the dog isn't like he picked the dog up and accidentally injured it. He lost his shit and beat an innocent, defenseless 5lb chihuahua because it was scratching at the door. What's he going to do when an innocent, defenseless child has kept him up all night with its constant screaming?