Sie brauchen eine andere Benutzervariable, die Ihnen mitteilt, wann es in einem neuen Monat ist.
SET @rownumber := 0;
SET @month := 0;
SELECT pla.event_date,
@rownumber := IF(@month=MONTH(pla.event_date), @rownumber + 1, 1) AS rank,
@month := MONTH(pla.event_date) AS month,
pla.kills, pla.player_id
FROM player AS pla
INNER JOIN ...
WHERE pla.event_date >= '2017-09-01' AND pla.event_date <= '2017-12-31'
ORDER BY MONTH(pla.event_date), pla.kills DESC
