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;