Violence is an extreme form of physical communication, and in both the instances of Arthur with Merlin in this episode and Uther with Morgana last episode violence is being used to emphasize a similar point, to wit, "You've found my last nerve, now back off." While I don't think Arthur had any intention of using it, there's a world of difference between waving a sword in someone's face and punching their arm. One is a threat, the other is not. I've seen things like that done IRL, and in many ways it's a silent plea for help. It's a way of saying, "Please shut up and take me seriously." Not a very good way, mind you, but that is the intent.

I wouldn't say their relationship is physically abusive, no. It's obvious Arthur isn't abusing Merlin in their regular relationship as master and man. But at this point we don't see the special relationship between the two acknowledged by Arthur except through manipulation and violence. That changes in the next episode, and that change might have to do with the talk Arthur and Uther had at the end of this episode.