Chess and literature are related in many ways. Both involve aesthetic considerations. To Nabokov, the "originality, invention, conciseness, harmony, complexity, and splendid insincerity" of creating a chess problem was similar to that in any other art." It's perhaps easier to theorize about beauty in chess than beauty in literature. It may be instructive too.
"Secrets of Spectacular Chess (2nd Edition)" by Levitt and Friedgood (Gloucester publishers, 2008) tries to categorize beauty in chess. It looks at chess games, chess studies (positions that might have turned up in games, but probably didn't) and chess puzzles (artificial positions). These are compared to "Real Life", Stories and Poetry respectively.
They use 4 main criteria
Economy and "tightness" also figure. For Chess Studies the artificiality of the problem matters. Some problem-creators strive for unity (maximising the shared elements amongst possible variations (aka interpretations?)). Truth matters too. In a section called "Beauty, Truth and the Computer" the book addresses the issue of whether refutation devalues the artistic merit, whether you can have Art for Art's Sake.
Finally they look at changing the rules of the game to offer new possibilities.