Cheating-agreed. No question about it.
From OP request for advice and support: It happened. Cheating is a terrible, hurtful thing to do to someone, and I am sorry it happened to you. Many will say "strike one, you are out." Others may be more forgiving. But your decision is just that, yours.
From the brief description of the events, I believe he was probably blackout drunk. He was honest and upfront and appeared to be genuinely remorseful, which is a positive thing, and not typical behavior of an active alcoholic. And you mention that he does not drink often, again not characteristic of an alcoholic. So I don't think we can jump to the conclusion that he is an alcoholic. And regarding the hickeys- another point to the blackout. What rationally thinking person would allow a girl to give him a hickey if he would be returning home to his girlfriend?? Even in the throws of passion, you KNOW when something will result in a hickey, and you KNOW it will be hard to explain away. He can't use the "I burned it with a curling iron" excuse.
But the fact remains, that he did cheat. No get out of jail free card due to alcohol. Tough decision no matter how you slice it...
Regarding the mean and verbally abusive part, that is another can of worms. I have known people that are not alcoholics, but on the rare occasion that they drink, they are just jerks, and do stupid things. They should come with a label that says "Instant A$$hat - just add alcohol."
Any chance for couples counseling?