I take it that (Index1, Index2) is a unique key on Table, otherwise I would expect the reference to t.SpecialEventCount to result in an error.
Edited query to use subquery as it didn’t work using GROUP BY
UPDATE
Table AS t
LEFT JOIN (
SELECT
Index1,
Index2,
COUNT(EventType) AS NumEvents
FROM
MEvents
WHERE
EventType="A" OR EventType="B"
GROUP BY
Index1,
Index2
) AS m ON
m.Index1 = t.Index1 AND
m.Index2 = t.Index2
SET
t.SpecialEventCount = m.NumEvents
WHERE
t.SpecialEventCount IS NULL