単一のテーブル内の各カテゴリのmysqlSELECTベスト

これを試してください：

SELECT gamers.*
FROM gamers
INNER JOIN 
 (SELECT 
   max(score) as maxscore, 
   gameid from gamers
   GROUP BY gameid) AS b
ON (b.gameid = gamers.gameid AND b.maxscore=gamers.score) ;
ORDER BY score DESC, gameid;

これにより、次のように出力されます：

+---------+--------+-------+
| gamerid | gameid | score |
+---------+--------+-------+
|       4 |      1 |    90 |
|       5 |      2 |    40 |
|       8 |      3 |    30 |
+---------+--------+-------+
3 rows in set (0.00 sec)

実行できる他のオプションは、一時テーブルまたはビューを作成することです（サブクエリが気に入らない場合）。

create temporary table games_score (
 SELECT max(score) as maxscore, gameid FROM gamers GROUP BY gameid
);

次に：

SELECT gamers.* 
FROM gamers 
INNER JOIN games_score AS b ON (b.gameid = gamers.gameid AND b.maxscore=gamers.score) 
ORDER BY score DESC, gameid;

またはビュー：

create or replace view games_score AS 
SELECT max(score) as maxscore, gameid FROM gamers GROUP BY gameid;

次に：

SELECT gamers.* 
FROM gamers 
INNER JOIN games_score AS b ON (b.gameid = gamers.gameid AND b.maxscore=gamers.score) 
ORDER BY score DESC, gameid;