Aesthetics carries two distinct meanings in game design literature and the two should not be conflated.
In MDA, aesthetics are the desirable emotional responses evoked in the player — sensation, fantasy, narrative, challenge, fellowship, discovery, expression, and submission (Hunicke, LeBlanc & Zubek 2004, see source-mda). The designer’s goal is to engineer mechanics and dynamics that produce the target aesthetic experience.
In Schell’s Elemental Tetrad, aesthetics refers to the sensory presentation of the game — its look, sound, and feel (Schell 2008, see source-art-of-game-design). This is closer to the everyday meaning of the word.
When reading game design writing, check which sense is intended. MDA aesthetics = emotional outcome; Tetrad aesthetics = sensory surface.
Related: mda-framework, elemental-tetrad, mechanics, dynamics, game-feel