Only skimmed the timeline quickly of the video quickly (ticker headlines gave a good indication of events) and the script seems to roughly follow modernized equivalent events of the first hour of the movie The Day After from 1983. (a worthy watch but not really for enjoyment) https://www.youtube.com/watch?v=Iyy9n8r16hs
Do yourself a favour and never watch the BBC Movie from the 80s called Threads about a nuclear war breaking out. Incredible movie but by far the most depressing thing I've ever watched. I felt down for days after watching it during college one time. Never been so effected by a movie. Quite a remarkable piece of work.
Another is Countdown to Looking Glass. It starts out as being told through live news reports although I guess the writers couldn't find a way to maintain that type of storytelling through the whole movie.
Although it's not nuclear war, a better example in the same vein is Special Bulletin.