When the pub is closed, no new pieces may enter it, and any piece that can leave the pub by a legal move must do so. Running pieces may not cross pub squares, but jumping pieces (for example, the N or the HFD) may do so. Notice that if you are in check, you need not move out of the pub and thereby lose your King -- leaving the pub would not be a legal move because of the check -- but if, for example, your Queen is attacked while some piece can leave the closed pub, you have trouble. If multiple pieces can leave the pub you may choose which one does so first.
The pub is closed on moves 8, 9, 10, 18, 19, 20, and so forth.
The point of this game is that the strategical advantage of centralizing is counterbalanced by the disadvantage of possibly being forced to exit at an inconvenient time. If you think for a while about the tactical possibilities of this type of forced move, you will realize that Closing Time is a good game.
It's not a great game, I think, but if there were a "Chess Variant Tournament", where the players had to play randomly chosen good games, Closing Time would be good enough to be on the list. (The point of a "CV Tourney" would be to test the general chess variant ability of the players; some players specialize in Progressive and its subvariants, but are not very good at Avalanche, other players are tops at Chessgi but can't play Alice, but a tournament played with a list of good games which are less often played would take away the advantage of specialists. The more good games there are to choose from, the better the tournament works, and so every new game as good as Closing Time has value.)
Closing Time is a board, not a game, and therefore you can play Closing Time Shogi or Closing Time checkers.
Closing Time appears to be value-preserving, and therefore you can play Closing Time Chess with Different Armies.