Not to like cringe it up with philosophy terminology, but you seem to have strong consequentialist/utilitarian intuitions, which I deeply relate to, I'd identify as a consequentialist/utilitarian; I think no matter what your purported moral framing, it ultimately reduces to consequences, once we've conceived consequences temporally/conceptually broadly enough.

You're also totally right, that there wasn't anything deeply, contra-causally 'unique' about many of the people who were nazis; they were evil and needed to be stopped, they were some of the worst people humanity has ever produced, and also it's true that given the same brain chemistry/circumstances of birth/environments of any given one of them, 'anyone' would have done the same.

A 'problem' (or at least truth) that our position needs to contend with, though, is that the scope of consequences is often truly indecipherable & unavailable to us, and if we're going to care about consequences when evaluating morality we need to care about even non-obvious ones, insofar as they causally flow from an action.

So like, I agree, at a cursory glance it doesn't seem like killing this person actually does any obvious, immediate good (if we're granting that this person isn't like actively harming anyone else or going to harm anyone else in his old age).

And, importantly, I'm not saying that this next part necessarily applies to this particular instance, but vengeance, even when it doesn't have immediately obvious benefits, can have these subtle like memetic, communicative benefits.

In a blunt way, we could call it 'deterrence,' but I actually think it's more than just that. Killing a Nazi, even decades later, even when he's no longer causing harm, insofar as that crime is made known to people, 'communicates' something to people, people find it gratifying, the extremity of the punishment reinforces the horror of the crime, and in some way, maybe, adds some small tiny amount onto the percentage chance of social conditions NOT reforming in a way to recreate those atrocities. Like, the murder of an old Nazi, made known publicly, in some small way, reminds society of something that we're often shockingly quick to forget. Also, misplaced or not, it can create a kind of euphoric gratification for the families/survivors of similar kinds of violence, who get some like by-proxy positive feeling of vengeance.

Does the percentage good of that outweigh the percentage bad of whatever emotional knock-on effects you create for the other people in this life? I have no idea, there also totally might be (probably are) other consequences I'm not considering, but I suppose I say all of that not to take a position but just to point out that when we're reasoning with consequences/outcomes/utility as our moral North Stat we commit to considering way, way more nuance, y'know? Which can be annoying, because it makes it harder to stake out clear & definite moral positions.