I agree this is an interesting take on chess. Didn't have the opportunity to play against someone different than me though. From what I have gathered so far the situation that both sides can beat one of the other player's pawns, do this move and end up beating nothing because the pawns wanted to beat each other seems to be quite common.
Liked the music and the sounds, and the move indicators are a treat. So the only suggestion I have at the moment is to enable actual parallel play by allowing the players to play on different devices.