How about this? It's a little dirty but I think it does the trick.
SELECT T3.id, T3.game, T3.point
FROM TableName AS T3
INNER JOIN
(SELECT T1.game, MAX(T1.Mpoint) AS RPoint
FROM
(SELECT game, MAX(point) AS MPoint
FROM TableName
GROUP BY game, point
HAVING COUNT(point) = 1) AS T1
GROUP BY T1.game) AS T2
ON T2.game = T3.game
AND T2.RPoint = T3.point;