Try:
UPDATE STUDENT s SET points = s.points + CONSTANT * (SELECT p.score FROM PLAYSIN p WHERE p.name = s.name) Table aliases are a very good habit to have.
Using an implicit cursor alternative:
FOR rec IN (SELECT s.name, s.points + CONSTANT * p.score 'points' FROM STUDENT s JOIN PLAYSIN p ON p.name = s.name) LOOP UPDATE STUDENT SET points = rec.points WHERE name = rec.name END LOOP;