BIG BAD WOLF: Oh, it'd still be dark all right. It'd be more like Kliegspiel than Dark Chess. The same situation is possible in Kliegspiel in that if you move your King into check one the assistants watching the game will tell you that the move is illegal, but won't give you any details. In Dark Chess, your opponent takes your King and the game is over.
I think a dark version of Backgammon would work, though I'm not sure if it'd be a fun game or not. I'd give it a try if it was here. Sure, I'd try different moves to investigate if a point was guarded. Remember you would only be able to do this with the dice that you roll.
An alternative to having the whole board dark except where your pieces are would be to show all those points that are available to be moved to with the current dice roll. This would save the time and trouble of checking every move possible. In Dark Chess you can see the squares that your pieces can move to. If you block a piece or move it to a different place, the view will change, but not until you have made the move and it is too late for you to undo the move. Depending on the roll, it could be very illuminating or not so much. 1-1 for example. Also, would your opponent be able to see what roll you received? If so, he'd be able to figure out what you know of his position and maybe plan, trap, or play accordingly. At the start of the game you'd know your opponent's position. I'm thinking that after just a few moves it'd be real dark and you'd need to see where the pieces might be with the help of the rolled dice.