Honestly, the Eminians could have at least made the effort to get the Enterprise
crew excused from the disintegration chambers. That could have been the first piece of the puzzle to bring the two sides together...
"Hey, we've got a ship in orbit that isn't one of ours that got caught up in an attack. We need to amend the treaty to exempt extra-system ships from our wargame since we're seeing more and more traffic. Or else someone is going to come in and end this game permanently."
Of course, then you don't have an episode.