What does this writer mean?
As Bryan indicates, this question is hardly answerable in the context of science. However, I can take a bash at it;


  Can anyone explain what she means by this? Isn't the melancholic, in the last analysis, the same as the depressed?


No, melancholy is more of a 'normal' emotional state, whereas depression is a debilitating mental illness associated with morbid symptoms and higher chances of suicide.  

As to that other passage, I reckon that's really a biased, opinion-fueled statement with no relation whatsoever in science. To cite a part of the wiki page on her: 


  Her [...] work includes [...] intertextuality, the semiotic, and abjection, in the fields of linguistics, literary theory and criticism, psychoanalysis, biography and autobiography, political and cultural analysis, art and art history.


These areas of expertise are quite far from science. Psychoanalysis comes closest, but even that is disputed in terms of not being embedded in evidence-based science.