Dramatic
Okay, so this play is written in a dramatic style because it's a drama, yes (more on this over in the "Genre" section), but what we're referring to here is how dramatic the writing is—as in how often the language takes a turn toward a sort of look at me vibe. This is perhaps clearest when Elesin and Iyaloja get going with the parables and metaphors, or when characters break into verse.
For instance, Elesin clearly thinks he's hot stuff when the play begins, and he ponders and gets all puffed up about his crucial role in the rites and traditions involving the king's death. Check him out:
My rein is loosened.
I am master of my Fate.
When the hour comes
Watch me dance along the narrowing path
Glazed by the soles of my great precursors.
My soul is eager. I shall not turn aside. (1.36)
Not exactly shy and retiring about his importance in the world, is he? And, as you can see from that passage, he and his language definitely have a lot of flair and oomph—Elesin is packing in the dramatic effect big time.