This short story by Sarah Orne Jewett is written in the third person. This is indicated by the fact that the narrator does not present herself as a person within the story who has personally witnessed the events—the narrative does not take the form "I saw," "I thought," and so on. Instead, the main character, Old Miss Porley, is discussed in the third person, as "she," and her activities and thoughts are described by an external narrator.
We can be more nuanced than this, however, in discussing the point of view of a story. A third person narrator might be omniscient—somebody who knows the thoughts and feelings of all participants in the story, as well as everything that is going on in the broader universe, unconstrained by what the characters in the story might know or feel. This type of narration can also be limited, either to the perspective of one character or to the perspective of several.
This narrative opens very much from Miss Esther Porley's perspective. She is the focus of the narrative: we know that she was "shaky and excited" and was "fond of the minister's wife," for example. However, there are also sections of the narrative which do not concern Miss Esther Porley, and about which she could not have known. In section II, for example, we witness a committee meeting "which settled Miss Esther Porley's fate." This section is not written from any particular person's point of view; the narrator is third person omniscient. In section III, we meet another limited third person perspective in the form of Mr. Rill, who "knew . . . that he was getting stiffer and clumsier" as he journeyed towards Daleham.
As such, we can describe this story as being told from several different third-person perspectives. While the majority of the narrative is written in the third-person limited perspective of Miss Porley herself, there are also sections of omniscient narrative and sections where we see the limited perspective of other characters.