p.boxed
  | Both players play a move "at the same time".
  | Conflicts are resolved following a few simple rules.

p.
  In order to not rethink a big part of the code, the white move has to be
  played before the black one. However, the black player doesn't see it.

p So both players play "at the same time". Resolving rules:
ul
  li.
    If both moves arrive on the same square, both pieces disappear except
    if one is a king. In this case only the king remains.
  li.
    If a capture was intended but the target moved, the move is still played
    but doesn't capture anything.
p.
  Such captures can be anticipated by capturing our own pieces.
  If the enemy captures as predicted, his piece disappears.
  If he doesn't, the self-capture isn't undone.

figure.diagram-container
  .diagram
    | fen:rnb1kbnr/ppp1pppp/8/3qP3/8/8/PPPP1PPP/RNBQKBNR:
  figcaption After 1.e4 d5 2.e5 Qxd5 (anticipating 2.exd5 which isn't played)

h3 End of the game

p.
  Due to the simultaneity, it is possible that a king is captured for example
  after escaping a check in a wrong way, as the following diagram shows.
  So, capturing the king counts as a win, of highest priority.
  A checkmate wins too, but if your king is captured and the other still on
  the board (even if it is mated), you lose.

figure.diagram-container
  .diagram.diag12
    | fen:r3r1bb/ppqRkppp/8/2p1n3/7n/8/PPPPP1P1/RNBQNBK1:
  .diagram.diag22
    | fen:r3r1bb/pp1qRppp/8/2p1n3/7n/8/PPPPP1P1/RNBQNBK1:
  figcaption.
    Left: before Rxe7 (white) and Qxd7 (black)
    Right: after the move (1-0)

h3 Source

p
  a(href="http://www.hexenspiel.de/engl/synchronous-chess/") Synchronous chess
  | , modified to allow en-passant captures
  | and disable the "exchange of captures" stage. 
  a(href="http://www.pion.ch/echecs/variante.php?jeu=synchro") Another description
  |  (in French).