I don't think the idea of "closure" is necessarily uniquely American but you hear an awful lot of people in the US seeking it. Closure, as mentioned in the article, can indeed mean revenge but in many cases that are civil in nature, a judgment or settlement is often unsatisfactory to one side or both.
It is hard for people to accept that what is often needed in addressing the extreme trials and tribulations in life, is to quantify the exposure or pain and contain it so we can live with something that is more manageable.
So many things in life affect us in a way that is not black or white. Think of how many diseases are chronic and can only be managed but not cured. And in life itself, no one gets out alive.
But people often talk in terms of winning wars, beating cancer, winning an argument. We have to live with the outcome of things and have to write a narrative that lets us sleep. This narrative often bends and corrupts the truth so that we can reconcile such inscrutable things as good and evil.
If such practice helps people to live with the uncertainty of life, then it can be helpful, but self deception, taken too far, almost never works out well in the long run. And when self deception rises to the level of group think, revolutions sometimes occur, with whatever consequences that entails.
Interesting article topic.