Maybe someone who still has an early VHS release could enlighten us.
I just looked at the VHS the scene as you described is not shown. The holocaust is discussed in later scenes and Buck goes out to see the ruins of Chicago in which Dr. Theopolis on Twiki tells Buck about the horror of it, but no footage of the 1987 war.
I wonder if it could be a deleted scene that was shown at a convention years after the fact, and THAT is what the OP is remembering? I have both the broadcast and theatrical versions on DVD, and neither have it.
Right after I first frond this thread, I went looking for my copy of the novelization, hoping to find the scene there, but now, I can't find the book. The only thing I DID discover is that my bookcases are not filed the way I thought they were.