In French logic, he does not grill the brochette. The heat, the fire grills it. He makes them to grill.
Il fait griller la brochette. Very similar to Je fais bouillir l'eau.
At least this is my understanding, based on my memory of earlier lessons on Duolingo. The intransitive verb can't take an object, so the verb faire is added to take it.
Because French people like using "faire" attached to a number of their verbs. For example taking a walk is "faire une promenade", cooking is "faire la cuisine" and so on. It's like in English when you say, "do the dance" You might as well say "dance" without the "do". It is therefore not mandatory even in French.