This is a premise that the restaurant owner uses to demonstrate that the critic isn’t a true restaurant critic. She uses the analogy of a drama critic to show that special expertise is required to be called a “true critic.”

This is support for the restaurant owner’s claim about the critic not being a “true critic.” A background in political reporting is very different than expertise in food and food preparation.

The restaurant owner concedes that the critic is a good writer but maintains he isn’t a true critic. This is neither a premise nor a conclusion.

This is what the restaurant owner is arguing for. Since the reporter lacks expertise in food and food preparation, and since newspapers wouldn't call someone a drama critic if the person has no special training in theater, the reporter isn’t a true restaurant critic.

This is a premise used to show why the reporter in question isn’t a true critic. The author references drama critics to imply that special training in a field is required to be a true critic in that field.