For the record, although I wasn't in the game myself, I think cancelling is clear-cut the right decision to make. That said, the decision should be in the hands of all players in the game (and if the mods are the ones to execute that decision that's perfectly fine).
But the names of the cheaters ought be given at the very least to their immediate victims in this game, and, possibly, the other players at large.
I think a good solution to this issue, for the future, might be to create a new voting option, perhaps called "No Contest," wherein the game is cancelled, like a cancelled game would be, but the game DOES NOT disappear from records. Instead, much like any game at its end, the map would read "No contest" (as opposed to "Game drawn" or "Game won by X"), the anonymous players would be revealed, and the game itself would still exist on record. This would be useful in the following situations:
* Games ruined by cheating: Not only does this option reveal the cheating parties and leave on record proof of their cheating (a benefit which should be self-evident), it also leaves their specific in-game maneuvers available for people to see. This is likely not especially important, but if there is a benefit to people cheating, it's that we get to see what two countries might do if they could be assured of perfect collaboration with one another. Suppose hypothetically that the Sealion were first discovered by cheaters playing France and Germany. What a loss it would be if such a fascinating and powerful opening were lost forever because the game was cancelled and wiped from the records.
* Test games: Back in 2011, I did extensive play-testing of the major 1v1 variants with Gobbledydook. This has slightly inflated my number of draws -- we needed to record the games for further study so we could figure out optimized strategies, and the Concede button didn't exist yet, so the only way to end the game immediately and keep it on record was via Draw. (Of course, the Concede button suffers from the same issue, inflating wins and defeats instead of draws.) Further, just recently I played a test game with fasces, and we drew after abandoning the test. Fasces was set to win, frankly, and had a much better position on me, but the game is (in my mind) erroneously considered a draw on the record instead of a no-contest. It would be useful to have no-contest as a potential result so that we can study the game and learn more from it without worry about the game affecting player stats or being lost from the record.
* Games we just plain want ended: Granted, the Cancel option exists for games like these -- but suppose that the players want the game to be available for later viewing, whether for study (as previously mentioned) or just plain nostalgia. It would be useful to have a no-contest option to preserve the game without it affecting records.