I was just reporting that you may have missed the affair bit. He says he went about things badly, but she knew all about it, it does not equal affair in my eyes. If you got it wrong and missed it, you got it wrong. Nothing wrong with admitting that but you can't really accuse him of having an affair as it is clear a) that was his wife and b) she knew about his relationship but as he says, he got carried away by NRE. He doesn't go into enough details for anyone to make a specific judgement and accuse him of cheating.
So no, it is not arbitrary. There is a very distinct definition, so you are splitting hairs.