^ That merely suggests that replicator technology became available years after TOS.
Actually, that merely suggets a lighted shelf where Kirk kept his dirty dishes. Maybe the yeoman didn't come by and pick it up yet. How long were they sitting there? The ship only just left space dock, Kirk didn't have time to scarf down a full meal. Was that breakfast before the meeting? If that was a replicator, why didn't he hit the button and get rid of the dishes? Is he that lazy he can't hit a button? Honestly, his quarters looked like they stank.
Odds are it's a food synthesizer, only they don't have the sliding doors anymore. Considering there IS a galley with cooks in this movie.