Get Position of row from query
This should work: 

SELECT pos, SteamId
FROM
(
    SELECT (@pos := @pos+1) pos
        , Map, Time, Date, SteamID
    FROM `surf_times` S
        , (SELECT @pos := 0) p
    WHERE `Map` = "surf_mesa" 
    ORDER BY `Time` 
) `surf_times`
WHERE `SteamID` = "76561198065863390"
ORDER BY pos
LIMIT 1;


SQL Fiddle