I think I especially like the idea of utilising other forces of war for an army. Chess is a very much a simplified version of classical warfare so perhaps I might use those ideas for future variations 
Interestingly, I saw a video on what space warfare might look like given actual physics. The mechanics of such a realm was very interesting in my opinion and obviously conducted within a 3D space. Whatever you might think of the guy, the "Space Force" was actually one of my favourite ideas of the former US president with very legitimate reasons for branching out this way (due to the need for greater control over satellite, observation and communications that are necessitated for better cohesiveness in modern warfare).
Watch this space, I will make Space Chess :0
Chess is a millenary old game that allows human minds to challenge each other and practice the art of war, without actual bloodshed. It always enjoyed an extraordinary success for some of its specific characteristics. Among these: the huge number of possible positions and moves; the balancing of forces in the field; the balance between forces and available spaces.
Chess players are commanders who deploy their own army, engage the opposing army and devise any possible strategy and tactic to win that battle. All this is inspired by the military art of past centuries, when battles were won by geniuses of strategy and tactics such as: Alexander the Great, Hannibal, Genghis Khan, Napoleon, and the like.
However in the real world of today, battles are no longer conducted in this way, i.e. on a flat field. Strategic and tactical elements that exploit the three dimensions of space have become crucially important: airplanes, helicopters, drones, missiles, satellites, spacecraft, etc., are the elements with which today's battles are won; not counting different realities that may belong to other dimensions, such as intelligence, communications, cyberwarfare, etc.
Therefore, we see a growing desire to try and practice an art of war that is more consistent with the complexity of today's challenges. With the aim to give answers to this desire, several variants are presented that try to upgrade the game of chess, in order to reflect the evolution towards a greater complexity of the world. This is how variants of chess in three or more dimensions are born.
Obviously adding a dimension multiplies the available space and makes an already much complex game enormously more complex. Pieces, for example, increase their mobility and thus their strength. They themselves become inherently different, since their possibilities are increased. More space available allows for more pieces and possibly more types of pieces.
Players' minds must exercise on much more complex realities, resulting in challenges of a higher level. Many players can feel lost in the complex space; but actually it's the same feeling we had when we were kids and tried chess for the first time.
Minds also cannot rely much on theory, but practically only on their own reasoning, at least until a much more complex theory is developed specifically for a game of this kind. For a certain period it will be like playing chess in ancient times; before a theory for this game was developed. If someone wants to relive that feeling, this is the right place to present and discuss ideas, as well as to try out new types of games.