I bet Moiraine played Snakes and Foxes when she was young and by her knowledge of the game and the doorframe in Tear, had a pretty good guess of the one in Rhuidean. Plus, if she saw different futures of the way things could be and the way things had to be in the arches in Rhuidean, I'm sure she seen some of the things that happened within that doorframe or she wouldn't have known to write that letter to Thom in the first place.