The alias should be included after the DELETE
keyword:
DELETE th
FROM term_hierarchy AS th
WHERE th.parent = 1015 AND th.tid IN
(
SELECT DISTINCT(th1.tid)
FROM term_hierarchy AS th1
INNER JOIN term_hierarchy AS th2 ON (th1.tid = th2.tid AND th2.parent != 1015)
WHERE th1.parent = 1015
);