The Monster sees himself as an Adamic character because he is "apparently united by no link to any other being in existence" (Shelley 117). Adam from Paradise Lost is also alone before Eve is created; thus, Adam and the Monster see no one around who looks remotely similar to them.
However, if you read further in this chapter (15), the Monster bemoans the fact that his creator, unlike Adam's, did not make him perfect or superior. Instead he is "wretched, helpless, and alone." He states that he identifies more with Satan because when he looks at the happiness of his "protectors," envy fills his soul, just as Satan in Paradise Lost longs for recognition and power.