If you want it in a single query, initialize the variables in a joined subquery
SELECT
, (@csumA := @csumA + A) as cumulative_A
, (@csumM := @csumM + M) as cumulative_M
, (@csumE := @csumE + E) as cumulative_E
, (@csumW := @csumW + W) as cumulative_W
FROM (
SELECT WEEK(s.date) week,
SUM(CASE WHEN s.user_id = 50 THEN s.points ELSE 0 END) AS A,
SUM(CASE WHEN s.user_id = 51 THEN s.points ELSE 0 END) AS M,
SUM(CASE WHEN s.user_id = 52 THEN s.points ELSE 0 END) AS E,
SUM(CASE WHEN s.user_id = 53 THEN s.points ELSE 0 END) AS W
FROM users u
JOIN scores s ON u.user_id = s.user_id
JOIN league l ON l.league_id = s.league_id
AND and l.league_name = 'Sunday League'
WHERE year(s.date) = YEAR(sysdate())
GROUP BY s.date ORDER BY s.date ASC
) PTS
JOIN (
SELECT @csumA:=0, @csumM:=0, @csumE := 0, @csumW:=0
) INIT;