MySql remove counted value from another count
There are multiple ways to achieve that

Repeat the expressions in the new column definition:

SELECT `GameID`, 
count(case `Liked` when 1 then 1 else null end) as likes,
count(case `Liked` when 0 then 1 else null end) as dislikes, 
count(case `Liked` when 1 then 1 else null end)-count(case `Liked` when 0 then 1 else null end) as diff
FROM `rating`
GROUP BY `GameID` 
ORDER BY diff DESC


Wrap it in another query:

select GameID, likes, dislikes, likes-dislikes AS diff
from (
    SELECT `GameID`, 
    count(case `Liked` when 1 then 1 else null end) as likes,
    count(case `Liked` when 0 then 1 else null end) as dislikes
    FROM `rating`
    SET likes = likes + dislikes
    GROUP BY `GameID` 
) as tmp
ORDER BY diff DESC