This is a very interesting question to consider, because of course the writer of this text wrote it about 1600 years before the term Romanticism was even heard of or conceived. Yet it is right to recognise the way in which the ideas about sublimity represented in this treatise in many ways act as an important precursor to Romanticism. Longinus for example describes the effects of sublime literature in terms that find an accurate and eerie parallel with Romantic expressions of what literature should do in terms of its transformative and transcendental properties. Note the following description that Longinus provides of what sublime literature should do to its reader:
For, as if instinctively, our soul is uplifted by the true sublime; it takes a proud flight, and is filled with joy and vaunting, as though it had itself produced what it has heard.
Longinus, through his description of sublime literature "disposing the soul to high thoughts" argues that good literature should be literature that is Romantic in the way that it captures timeless truths about the human condition and expresses them in such a way that the reader is transported and understands something about the key condition of being human. Sublimity, with its emphasis on natural expression and impulse, balanced astutely with skill and artifice, is something that sounds awfully like Romantic poetry and literature. It is therefore perfectly plausible to argue that Longinus was in fact the first Romantic critic.