Do you think it's possible to appreciate 'The Great Gatsby' (2013) as an adaptation of the Fitzgerald novel, or solely as a film in its own right (if at all)?

I'd say that it was an adaptation of the book. Although the movie also had differences (like Nick's prologue and epilogue as an alcoholic trying to find peace), the similarities are too much for it to not be based on Fitzgerald's novel and dismiss it as a movie of its own.