fix(know-your-world): guard against undefined state during session init

Add loading guard in GameComponent to prevent crash when state is
undefined during session initialization.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

apps/web/src/arcade-games/know-your-world/components/GameComponent.tsx

@@ -27,6 +27,23 @@ export function GameComponent() {
     return () => window.removeEventListener(CROP_MODE_EVENT, handleCropModeChange)
   }, [])
 
+  // Guard against undefined state during session initialization
+  if (!state) {
+    return (
+      <div
+        style={{
+          display: 'flex',
+          justifyContent: 'center',
+          alignItems: 'center',
+          height: '100vh',
+          color: '#888',
+        }}
+      >
+        Loading...
+      </div>
+    )
+  }
+
   // Determine current player for turn indicator (if turn-based mode)
   const currentPlayerId =
     state.gamePhase === 'playing' && state.gameMode === 'turn-based'