You might also try updating an in-line view:
UPDATE (select s.name student_name,
s.points student_points,
p.score playsin_score
from STUDENT s,
PLAYSIN p
where p.name = s.name)
SET student_points = student_points + CONSTANT * playsin_score;
It also limits the rows in STUDENT that are updated to only the set for which there
is a row in PLAYSIN (you might also consider in your current code what happens to SCORE if that subquery could return NULL). You'd need a unique or primary key on playsin.name to use this syntax to avoid a join cardinality check error, but if this is not feasible then a MERGE statement might be useful. A MERGE might be worth considering anyway if you also have code to add into STUDENT any new names in PLAYSIN.