This query should get what you need:
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)
It assumes that a tie is a win for both players.
SQLFiddle
If you want to get just the player and their number of wins, you can use this query:
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
Just replace {player_id}
with the player you're looking for and wins
is their number of wins or ties.
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