War Drama
This is pretty much a no brainer: The story revolves around the dropping of the first atomic bomb during World War II (there's the "war") and chronicles the impact of that event on six individuals (there's the "drama"). So, we think "War Drama" is the most appropriate categorization here.
Of course, it's important to note that this is a journalistic account rather than a fictional "drama," but that doesn't make it any less dramatic; the reality of the Hiroshima attack and its aftermath is, sadly, plenty dramatic without any embellishments and fabrications.