refactor(matching): remove legacy battle-arena references

Remove duplicate game entries by cleaning up legacy GAMES_CONFIG references.
Matching game now accessed exclusively through game registry.

- Removed battle-arena from GAMES_CONFIG
- Removed battle-arena from GAME_TYPE_TO_NAME mapping
- Removed battle-arena navigation logic

Fixes duplicate game entries in game selector.

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

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

apps/web/src/app/arcade/room/page.tsx

@@ -9,8 +9,8 @@ import { css } from '../../../../styled-system/css'
 import { getAllGames, getGame, hasGame } from '@/lib/arcade/game-registry'
 
 // Map GameType keys to internal game names
+// Note: "battle-arena" removed - now handled by game registry as "matching"
 const GAME_TYPE_TO_NAME: Record<GameType, string> = {
-  'battle-arena': 'matching',
   'complement-race': 'complement-race',
   'master-organizer': 'master-organizer',
 }

apps/web/src/app/games/page.tsx

@@ -20,11 +20,10 @@ function GamesPageContent() {
 
   const _handleGameClick = (gameType: string) => {
     // Navigate directly to games using the centralized game mode with Next.js router
+    // Note: battle-arena has been removed - now handled by game registry as "matching"
     console.log('🔄 GamesPage: Navigating with Next.js router (no page reload)')
     if (gameType === 'memory-quiz') {
       router.push('/games/memory-quiz')
-    } else if (gameType === 'battle-arena') {
-      router.push('/games/matching')
     }
   }
 

apps/web/src/components/GameSelector.tsx

@@ -7,22 +7,8 @@ import { getAllGames } from '../lib/arcade/game-registry'
 import { GameCard } from './GameCard'
 
 // Game configuration defining player limits
+// Note: "matching" (formerly "battle-arena") has been migrated to the modular game system
 export const GAMES_CONFIG = {
-  'battle-arena': {
-    name: 'Matching Pairs Battle',
-    fullName: 'Matching Pairs Battle ⚔️',
-    maxPlayers: 4,
-    description: 'Multiplayer memory battle with friends',
-    longDescription:
-      'Battle friends in epic memory challenges. Match pairs faster than your opponents in this exciting multiplayer experience.',
-    url: '/arcade/matching',
-    icon: '⚔️',
-    chips: ['👥 Multiplayer', '🎯 Strategic', '🏆 Competitive'],
-    color: 'purple',
-    gradient: 'linear-gradient(135deg, #e9d5ff, #ddd6fe)',
-    borderColor: 'purple.200',
-    difficulty: 'Intermediate',
-  },
   'complement-race': {
     name: 'Speed Complement Race',
     fullName: 'Speed Complement Race 🏁',