愛する人 technically means either "the person one loves" (=one's beloved person) or "the person who loves someone", depending on the context. In this context it's the former because "protecting the person he loves" makes sense here but "protecting the person who loves someone" does not.
It is very common for verbs to be used like adjectives, and that's called relative clauses. Unlike English, Japanese relative clauses modifies something that follows. If you don't know Japanese relative clauses, please read this.
若者が 人を 愛する (a youth loves a person)
［若者が ＿＿ 愛する］ 人 (a person whom a youth loves)
Recently I introduced this post to you. Once you understand Japanese relative clauses, it should be more clear why some people say Japanese i-adjectives are grammatically more like verbs, and, in this case, why a normal verb looked like an adjective to you.