No, cuckoldry refers to an unfaithful spouse who slept with another man DURING the relationship and has kids. Having kids from another relationship is not cuckoldry, as it is understood outside of very specific evolutionary biological contexts. (Claiming it here would be Equivocation) Besides, it's irrelevant if someone falls in love and wants to get attached to someone. Just because you have kids DOESN'T mean you automatically get thrown out of the dating scene because of a divorce or because you're a widow. In fact, evolutionary, it's a good sign as it indicates fertility. You're overly focused on this bizarre notion that just having kids with another man at some point automatically makes you inferior in terms of a relationship, but that's not how humans work.
Also, adoption is relative to circumstance as some may want to do it simply because they like the kid or because they want to help people and adoption is a good way to ensure a better quality of life for them. Additionally, other personal reasons like being an orphan or being adopted themselves may be a reason, but this varies from case to case and is up to the individual to decide.
I think you are too quick to judge these things as I think most of these can't be simply dismissed because of the complexity of human interactions and how such things are not intrinsically bad if the party in question consents to it. The woman he fell in love with is not adulterous or cheating on him and he's not necessarily any less of a man or masculine figure for wanting to take care of a kid, even if it's not his and even if he's just entering this relationship. You may not want a partner who has kids, but to try and make it a blanket rule or block others for making that decision for themselves is a bit childish.
@supermoonchrome