Is the narrator as rich as Tricki's mistress?

No, the narrator is not as rich as Tricki's mistress. It can be inferred from various instances in the story that Tricki's mistress is very rich and leads a luxurious life. The author describes the kind of food she feeds Tricki, different accessories and clothes she keeps for Tricki, the servants in her house, etc. The narrator is not as rich as Tricki since at the end of the story when Tricki was almost fine and was about to go back to his mistress, the author mentions his slight intent of keeping Tricki so that he could get all the food the lady sends for Tricki. This shows that the narrator was not as rich as the mistress.