Toroidal Byzantine Chess is a no more than old Byzantine Chess played on toroidal rather than cylindric board. It appeared in 1999 or 2000 among the graduates of Moscow Aviation Institute as a variation of Byzantine or Circular Chess. (Both of them are also presented in "Zillions of Games").
 
The game as implemented is on a very large (600x600) board, so you will need to have your display properties set to at least 1024x768 to play.