Just because an addict can go "dry" for a spell, doesn't mean he's not an addict. Going and spending money on gambling every week when you have a family to take care of and a wife who has to work in a fast food restaurant sounds pretty much like an addict to me.
How much of the family money does he spend gambling?
Also - you are RIGHT to enforce a healthy boundary - he cannot live in the same house if he's going to continue his affair with OW. Virtual or otherwise.