Få Max værdi og tilsvarende kolonne

Denne forespørgsel skulle få det, du har brug for:

SELECT
    player_id, game_id, score
FROM
(
    SELECT game_id,MAX(score) AS MaxScore
    FROM games
    GROUP BY game_id
) AS Winners
JOIN games
    ON (games.game_id = Winners.game_id AND games.score = Winners.MaxScore)

Det forudsætter, at uafgjort er en sejr for begge spillere.

SQLFiddle

Hvis du kun vil have spilleren og deres antal gevinster, kan du bruge denne forespørgsel:

SELECT
    player_id, COUNT(*) AS wins
FROM
(
    SELECT game_id,MAX(score) AS MaxScore
    FROM games
    GROUP BY game_id
) AS Winners
JOIN games
    ON (games.game_id = Winners.game_id AND games.score = Winners.MaxScore)
WHERE player_id = {player_id}
GROUP BY player_id

Bare udskift {player_id} med den spiller, du leder efter, og wins er deres antal sejre eller uafgjorte.