"what amounts to a vicious cycle" means "a thing/situation/circumstance that amounts to a vicious cycle". "in" could be read as meaning that those people are in the situation described. Alternatively, and less literally, it could be read as presenting "what amounts to a vicious circle" as a description of the state arising from "their sense of personal worthlessness further diminishes their chances of gaining employment".
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park sang joonIn what amounts to a vicious cycle,In what is basically a vicious cycle, their sense ... etc.
park sang joon sure in their despair that no one will hire them.... as they feel sure (in that state of desperation) that no one will hire the
park sang joonsure in their despair that no one will hire them.sure that no one will hire them (because they are in despair).
tkacka15In what amounts to a vicious cycle.Is "what amounts to a vicious cycle" an object of the preposition?Yes.
tkacka15Another example: "The issue now becomes whether Tsipras was right to decide not to invoke this plan in the face of what amounted to extortion from the creditors." (Paul Krugman.)Good example.
park sang joonThen I'd like to know if I can regard #1 as either #2 or #3.#3