Historically, Mohammed did not write the Qur'an, he recited messages that he represented as delivered unto him in an angelological context. So physically, as initially communicated to his followers, the Qur'an probably didn't quite count as being in a "literary style," unless we expand that phrase to include things like "transcript of an oral tradition," say.
Arabic is an elegant language, there are calligraphic maneuvers possible within it (letters/words/text-blocks stylized as calligrams) that are not absolutely unique but are at least relatively unusual. And the Qur'an's role in the history of the Arabic language is comparable to the role of Shakespeare's writings in the development of English (possibly the former plays a stronger role in its language's presence than the latter, on account of the former's religiosity, but I digress). In a higher-order sense, then, one might say that the "metastyle" of the Qur'an is "a text that has played a dramatic role in its language's stylistic development." I'm not sure how often the end-of-section circles they use, or the stop-marker (when read, one is directed to an especial prayer), in the Qur'an, are used in Arabic composition besides, and again, it's elegant.
But there are plenty of elegant texts in other languages altogether, for that matter. How does the Qur'an not fall under the heading of "texts purported to be divine revelations"? Isn't that a style, on some level, too? (From what I have read of the Qur'an, I would say that it is only as unique as any other text tends to be, unique by being a particular, but everything is particular in its own way (that's what particularity is!). For otherwise, albeit I was reading it in English, but it looked not terribly dissimilar, in terms of tone/voice/style, from the Bible combined with the Shahnameh (a Persian/Zoroastrian epic poem, composed later than the Qur'an I think, but derived from a rich tradition).)