It can mean both sentences.
Suppose he forgets everything he learned in the classroom. Then "ele precisa de exercícios"
Suppose his health is going bad and he is getting fatter. Then "ele precisa de exercícios."
He needs to exercise is ok. And could be translated with "Ele precisa se exercitar" (only the "work out" idea is present here)
He could also practice exercises about some thing if you change the reflexive "se" by some other object:
Ele precisa exercitar seu Português - He needs to practice his Portuguese.
But why refuse "he needs exercise" after all these years of marking it as incorrect. Because the context is not given both "exercise " and "exercises" are correct. You site is simultaneously very helpful and annoying!. I have had to learn to give incorrect English translations in order to complete some lessons