As far as I'm aware they never explain the rules of Stratagema. I feel pretty comfortable saying it seems like a terrible esport to spectate. You've got
Basically, take a minimalist strategy game like Go and an RTS game and stick them together in a way that uses the strengths of neither. That's Stratagema. Don't play this game, it's dumb.
(Minor edit, after thinking this over a little it's possible the red pieces are neutral objectives. I don't think that correlates as well with the finger movements, but whatever. That'd just make Stratagema 3d Liquid War with mario kart powerups tacked on)
The weird 6 layer chess they have is just as baffling.
Edit: I did find this page though that explains it in great detail. http://meder.spacechess.org/3dschach/chess3d.htm
Haha
In these Laws the words 'he', 'him' and 'his' include 'she' and 'her'.
Wrap it up boys, inclusion achieved!