SQL/Access: Iterate through a query's results to use in another's WHERE clause
You can do this with a subquery to get your max score per game with the outside query pulling the details of the game.
FYI: This was tested in MS SQL, not MS-Access (sorry don't have that installed), but the syntax should be very similar.

SELECT t.* 
FROM tablename AS t 
JOIN (
    SELECT GAME, MAX(SCORE) AS MAXSCORE
    FROM tablename
    GROUP BY GAME
    ) AS MAXGAMES 
    ON ( t.GAME  = MAXGAMES.GAME 
     AND t.SCORE = MAXGAMES.MAXSCORE )
ORDER BY t.GAME ;