from fastapi import APIRouter, HTTPException
import uuid

games = []  # In-memory storage

router = APIRouter()

@router.post("/gaming")
async def save_game(
    game_name: str,
    genre: str,
    platform: str,
    rating: int
):
    """Save a new game to the database"""
    if request.method != "POST":
        raise HTTPException(status_code=405, detail="Method Not Allowed")

    game_id = str(uuid.uuid4())
    new_game = {
        "id": game_id,
        "name": game_name,
        "genre": genre, 
        "platform": platform,
        "rating": rating
    }
    games.append(new_game)

    return {
        "method": "POST",
        "_verb": "post",
        "message": "Game saved successfully",
        "game_id": game_id,
        "game_name": game_name
    }

@router.get("/gaming")
async def get_games():
    """Fetch all saved games from the database"""
    if request.method != "GET":
        raise HTTPException(status_code=405, detail="Method Not Allowed")

    return {
        "method": "GET",
        "_verb": "get", 
        "games": games
    }
```

This code provides two endpoints:

1. `@router.post("/gaming")` to save a new game to the in-memory `games` list.
2. `@router.get("/gaming")` to fetch all saved games from the `games` list.

The `save_game` function accepts the required parameters for a new game and creates a new dictionary entry with a unique `game_id` using `uuid.uuid4()`. It then appends this new game to the `games` list and returns a success response.

The `get_games` function simply returns the full `games` list.

Note that this is an in-memory storage example. In a real application, you would use a persistent database instead of a Python list.