There is a lot in Lundy Bancroft's writing about affairs being emotional abuse. But I don't count a confessed, one-off fling an affair if it wasn't pre-meditated. Infidelity yes but not an affair. All affairs contain emotionally abusive acts and so yes it does apply here because there are contributors having affairs who aren't in emotionally abusive relationships (just allegedly unhappy ones) and there's a poster who's having an affair with a married man who's emotionally abusing his wife by at the very least lying and altering her life without her knowledge.
I think there are people who commit emotionally abusive acts but that doesn't make them an emotional abuser. Just like there are people who have affairs who aren't 'unfaithful' for the rest of their lives. I've worked with people who were admittedly emotionally abusive in one relationship, but not in their next one. In my personal life I've also known people to have an affair and never go there again, either staying in their marriages or getting out of them. Not one of those people thinks that having affairs or emotional abuse is a good environment in which to raise children.
As for the people who only have the courage to leave their abuser when they've got someone else to go to - you wouldn't believe how many people end up right back where they started with a different flavour of abuser, because generally speaking, nice people with good intentions don't start a sexual relationship with a woman who's being abused. While she's still living with her abuser, a discovery or suspicion could cause an escalation. The best advice for a person exiting abuse is to spend time on her own helping her and her children recover, not jumping into another relationship. It didn't surprise me one bit that darkest's OM was emotionally abusive too.
For people who are in genuinely abusive relationships, there is help there for them to get out especially if children are involved. Because charities especially know how abuse damages children, even if the parents are saying the children are unaware. Just as there really are alternatives for women who've got no children and are fit and able to work. The elephant in the room is that the 'victim' often displays unhelpful and abusive behaviours of her own; retaliatory affairs, getting children involved in parental disputes, self-obsession, an all encompassing sense of victimhood and these damage children very badly too! They can get out of their relationships, just as their partners could but they don't want to lose material things and some don't want to support themselves and work, or claim benefits and feel they've 'come down in the world'. So their kids suffer. yes, their partners are just as much to blame for not ending the relationship either, but why put the responsibility on to someone else for your kids happiness? Or your own.
Leave.