fix(arcade): resolve TypeScript errors in game config helpers

Fixed three TypeScript compilation errors:

1. game-config-helpers.ts:82 - Cast existing.config to object for spread
2. game-config-helpers.ts:116 - Fixed dynamic field assignment in updateGameConfigField
3. MatchingGameValidator.ts:540 - Use proper Difficulty type in MatchingGameConfig

Changes:
- Import Difficulty and GameType from matching types
- Update MatchingGameConfig to use proper union types
- Cast existing.config as object before spreading
- Rewrite updateGameConfigField to avoid type assertion issue

All TypeScript errors resolved. Compilation passes cleanly.

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

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

apps/web/src/lib/arcade/game-config-helpers.ts

@@ -79,7 +79,7 @@ export async function setGameConfig<T extends GameName>(
 
   if (existing) {
     // Update existing config (merge with existing values)
-    const mergedConfig = { ...existing.config, ...config }
+    const mergedConfig = { ...(existing.config as object), ...config }
     await db
       .update(schema.roomGameConfigs)
       .set({
@@ -113,7 +113,10 @@ export async function updateGameConfigField<
   T extends GameName,
   K extends keyof GameConfigByName[T],
 >(roomId: string, gameName: T, field: K, value: GameConfigByName[T][K]): Promise<void> {
-  await setGameConfig(roomId, gameName, { [field]: value } as Partial<GameConfigByName[T]>)
+  // Create a partial config with just the field being updated
+  const partialConfig: Partial<GameConfigByName[T]> = {} as any
+  ;(partialConfig as any)[field] = value
+  await setGameConfig(roomId, gameName, partialConfig)
 }
 
 /**

apps/web/src/lib/arcade/game-configs.ts

@@ -10,13 +10,14 @@
  */
 
 import type { DifficultyLevel } from '@/app/arcade/memory-quiz/types'
+import type { Difficulty, GameType } from '@/app/games/matching/context/types'
 
 /**
  * Configuration for matching (memory pairs) game
  */
 export interface MatchingGameConfig {
-  gameType: 'abacus-numeral' | 'complement-pairs'
-  difficulty: number
+  gameType: GameType
+  difficulty: Difficulty
   turnTimer: number
 }