Right from the very start of this lesson series about sentences, we've been hammering home the idea of verbs, verbs, verbs. And yet here we are, learning about exclamations, and there's not a single verb in sight. So it's a valid question—are these really sentences?
They don't contain any clauses (the building block of sentences). But they do function at the same grammatical level as sentences, so functionally, yes, exclamations are a kind of sentence. They're the "strange uncle/aunt/cousin" of the sentence family.