We say the play is a drama because, umm…it's a play, a piece of literature that can only be fully appreciated when it's put in front of a live audience. More specifically we dub it a tragedy. Of course, Euripides the great rule breaker and genre bender, had his own ideas about tragedy – ideas that differed greatly from the concepts Aristotle would later pen in his Poetics.
For example, the protagonist of The Bacchae, the god Dionysus, has no hamartia, most often called a tragic flaw, but more accurately translated as a mistake in judgment. A hero or heroine's hamartia typically causes their undoing. This just isn't true with Dionysus.
Dionysus is a god, he can't do wrong, right? He sets out to punish the mortals who've denied him and gets just what he wants. Usually, a tragic hero suffers for his mistakes, but Dionysus emerges from the play triumphant. (You can read more about how The Bacchae doesn't fit the typical tragedy mold in "What's Up with the Ending?") We should note that that this isn't the first time this sort of thing happens in Euripides work. Just check out our guide to Medea for another example.