Glossary
Then a move is not legal if the moving unit remains in the same 4-squares area, that is, moves are only legal if they cross the grid lines. "Checks are fairy" i.e. a King is not in check if the enemy unit giving check could not "capture" the King under the grid-rules, that is, if it is in the same area.
There are some immediate consequences. A King or Pawn can never reach a corner. Kings can be in contact if they are in the same area. Consider the following (legal) position
Kings are not in check but Black is stalemate (Reader's exercise: Check this.)
There is only one White move that free Black. 1. Rh2?? and 1. Kd1?? would free Black but are not legal moves. 1. O-O-O?? would allow 1 ... Kxd2 and free black, but O-O-O is not legal because it would have the white King visiting a square (here d1) where he is in check. Only 1. O-O works.
Grid-chess has been invented by W. Stead in 1953. Different grid topologies can be used, but the 16 x 4-squares is the most common. Anyway, the chosen grid-structure is always visible on the diagram.
The Grid-chess condition is a powerful restriction on legal moves, so that it is well suited to retros. Here is a beautiful example:
A. Klibanski and N. Plaksin 2nd Prize feenschach 1977
13+10. (Grid-Chess) (a) Where have the missing men been captured? (b) First move of the Black King?