Garth Wallace wrote on Tue, Mar 1, 2016 11:46 PM UTC:
One way of making a toroidal chess playable (or a horizontal cylindrical chess, for that matter) would be to restrict passage across the border between the 1st and 8th ranks so each player's pieces could only cross in one direction (the 8-to-1 direction for white, 1-to-8 for black). That way the armies can begin in the standard array without starting in check.