mysql SELECCIONA lo mejor de cada categoría en una sola tabla

Prueba esto:

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;

Esto generará:

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

La otra opción que puede hacer es crear una tabla temporal o una vista (si no le gusta la subconsulta).

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

Entonces:

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;

O una vista:

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

Entonces:

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;