Ludo:
- Add endingGame guard to prevent double endGame calls
- Parse server winners from live polling (fixes empty leaderboard
  when opponent wins remotely)
- Fix win/loss detection: last place = loss (was broken for 2-player)

Chess:
- Add 5s failsafe timer: result screen shows even if network hangs
- Deduplicate navigation logic with navigated flag
- Prevent double-navigation if both .then and failsafe fire

Backgammon:
- Add scene.exitGameMode() to both result navigation paths
  (was missing, could leave UI in game-mode state)
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>