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I would not be convinced that the game, stripped of all "backstory", must get across the idea of the Holocaust.
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No, but it should be able to convey some of its intended themes without that. The act of herding humans like cattle, the administration of murder on a massive scale, the filtering of people on racial and cultural grounds, and the resources required to make it happen. Wielded confidently, game mechanics are surprisingly well-equipped to represent these sorts of things independent of any specific historical context.
From what was written about the game - and again if the game's complete rules tell otherwise I'd love to see them; only the props were given great emphasis in the article - those ideas only come across once you are told it's about the Holocaust. In fact, it was the author's intent to conceal that specific fact for the emotional gut-punch of the context switch at the end.
This is a parlor trick. The PS3 shooter Haze did it by lifting a drug fog from the player's eyes to reveal terrorists as freedom fighters, and no one thought it was particularly remarkable. Of course, people tend to pay more attention when you bring in the Holocaust. You get a lot of emotion out of people, almost automatically.
I'm saying we need to wield this power more responsibly. When an artist deals with the Holocaust, like it or not they are stepping into the territory of Elie Wiesel's "Night", Maus, Schindler's List, and Barber's Adagio for Strings. These are works of enduring depth that contribute greatly to our understanding of the tragedy. Train does not seem to sit well in their company.
I know games can do and have done much better than that, and I want us to continue to hold ourselves to that standard. If you think I'm offended simply because someone made a board game about the Holocaust, you could hardly have missed my point more completely.