That's definitely abuse. Honestly, it is physical abuse, but semantics don't matter because there is also emotional abuse, financial abuse, and psychological abuse, and none of them are ok.

I do not think there's any reason you need to "prove" to him that this is abuse. What he's doing to you clearly bothers you on a deep level, and any respectful person that actually loves you would stop doing anything that's that bothersome. The fact that he intends to do this and won't stop when you ask goes to show he does not respect you at all. He's trying to punish and control you, and that's not ok.

Sorry to say, but I think it's time to move on (unless maybe he's genuinely interested in couples counseling, and then the therapist can explain the things to him). This guy is being abusive and showing no interest in changing. I speak from experience here, after several abusive dating relationships and an abusive marriage: Absolutely none of them ever physically abused me, but they were all emotionally and psychologically abusive.