Yeah I hit a key and the cinematic ends, then there's just a black screen, if I wait nothing happens, if I hit a key I get to the screen showing time, kills, secrets found etc.
That's exactly what happens to me.... are you saying there should be another screen explaining the plot? That would go a long way to explaining why I was confused as to how the episodes connected to one another.
I noticed that in the first episode, I could hit a "help" key (I think it was F1) and it would display the "story" screen, maybe you can do that in other episodes and get the story screen that way?
EDIT: Youtube confirms that there should be some screens with text explaining the story, but I didn't get them with eDuke32 either. I've already finished the game so I can't go back and check, but maybe hitting F1 in different episodes will show you that screen. I don't know how to get it to show normally.