Think of Poe's writing in this story as having two parts: lines, or structure, and color. Kind of like a painter. Structurally, everything's clearly defined and logical. It's composed: it's "put together" from lots of individual units, which unite to build a larger whole. We say that because of how neatly the story divides on both the paragraph and the sentence level. Most of Poe's paragraphs are very short or very long, and each of the long ones describes a single thing: the first describes the Red Death, the second Prospero's castle retreat, the fourth (the third is short) describes the suite, the fifth describes the clock, and so on.
The paragraphs in turn are usually put together from lots of fairly short sentences that are structurally simple. They're like little atoms, each with just one or two details, which build up the larger whole. Sometimes the sentences just form something like a "list" of details. As in this paragraph:
There were much glare and glitter and piquancy and phantasm --much of what has been since seen in "Hernani." There were arabesque figures with unsuited limbs and appointments. There were delirious fancies such as the madman fashions. There was much of the beautiful, much of the wanton, much of the bizarre, something of the terrible, and not a little of that which might have excited disgust. (7)
Here, Poe's sentences are not only short, they're practically identical in their simple structure, beginning "there were" or "there were much."
Poe then infuses that clear structure with life by filling in the color. Much of the color and life in the writing comes from his word choice. Sometimes it depends upon the vividness or dramatic quality of the individual words: "arabesque figures," "delirious fancies." In other places, it's Poe's use of figurative language, like the alliteration between "glare and glitter" above. Poe's writing is filled with that kind of stuff; he has a real ear for language. And Poe's spot-on word choice just adds to the feeling of how composed and well put-together his writing is. Everything feels selected with the greatest care.
Every so often, though, Poe will produce one whopper of a sentence. Like this one, from the fifth paragraph:
Its pendulum swung to and fro with a dull, heavy, monotonous clang; and when the minute-hand made the circuit of the face, and the hour was to be stricken, there came from the brazen lungs of the clock a sound which was clear and loud and deep and exceedingly musical, but of so peculiar a note and emphasis that, at each lapse of an hour, the musicians of the orchestra were constrained to pause, momentarily, in their performance, to hearken to the sound; and thus the waltzers perforce ceased their evolutions; and there was a brief disconcert of the whole gay company; and, while the chimes of the clock yet rang, it was observed that the giddiest grew pale, and the more aged and sedate passed their hands over their brows as if in confused reverie or meditation. (5)
That sentence is a good example of just how thickly Poe puts in the details. He loves using lots descriptive words, even if the overall sentence or phrase is short. To describe the pendulum swing, for example, one adjective's not enough, Poe needs three: "a dull, heavy, monotonous clang."
Finally, we say Poe's writing is elegant because…do we really have to justify that? Just read it and tell us it isn't.