Clocks must not stop even when either of the player leaves the game

- Right now clocks just freeze where the are when either of the player leaves the game.

What is happening fine:
- The player who left the game loses when an opponent leaves the game after a fixed timeout.
- The game can be continued when an opponent rejoins the game.

Start by tracing the TypeScript server logic for player leave, clock updates, timeout losses, and rejoins. Reproduce a leave-and-rejoin game, then verify that the clocks continue running while a player is absent and that the existing timeout behavior still works.

Written by the indexing model from the issue text.