This is an interesting statement to consider, because psychology as a discipline and an approach was something that had not been conceived of at all at the time of writing of this text, and it would therefore be somewhat anachronistic to argue that this treatise was primarily psychological in its approach. Indeed, it would also be erroneous, as the true subject matter of Longinus is literary criticism; how to identify sublimity in literature and then advice on how to achieve it in one's writing. The emphasis that is given to a discussion of examples of literature that Longinus feels are good examples of sublimity or poor examples of it likewise support this view.
However, it is possible to argue that there is slight emphasis given to a psychological approach through the way in which Longinus seeks to classify and define sublimity and in particular through his description on the impact it has on the reader. Note how he describes this impact when the reader reads a piece of literature that is truly sublime:
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.
The description of the response of the reader to sublimity seeks to describe the effect of such literature in curiously psychological terms through its comparison to flight. It is possible to argue therefore that this treatise could be considered to use a psychological approach in the discussion of what sublimity does to the reader and how it elevates the soul and allows the reader to transcend their limitations. However, this would be the only area in which such an argument would hold credence.