No, he doesn't owe that loser an apology for threatening imouto Char. But he owes the girls an apology for taking their challenges away.
Although at this point, he should really just give principal Teresia her powers back and let her be - she should clearly see by now he does not threaten world peace. In fact, she may be happier and more fulfilled by applying herself to educate him further in the ways of the gods after graduation and after this "war" instead.

All he has to is unify the human and demon realm under his rule and world peace can be achieved - at the expense of his leisure and freedom.