The point of view in which Crane writes is third-person limited omniscient. A third-person point of view specifies an external narrator who is witnessing the story as though from afar, either at a near distance or a remote one. The narrator is not an agent in the story and does not participate in the story. This narrator witnesses the story and reports on it as it unfolds.
A limited omniscient third-person point of view means that the narrator has access--if desired--to focusing the thoughts, motives, and feelings of any one of the characters. Though the narrator in "The Open Boat" doesn't delve into psychological depths with the men in the boat, this omniscient knowledge of and insight into all characters and the accompanying broad view of surroundings and events is illustrated in this passage:
The crest of each of these waves was a hill, from the top of which the men surveyed, for a moment, a broad tumultuous expanse; shining and wind-riven. It was probably splendid. It was probably glorious, this play of the free sea, wild with lights of emerald and white and amber.
"Bully good thing it's an on-shore wind," said the cook. "If not, where would we be? Wouldn't have a show."
"That's right," said the correspondent.
The busy oiler nodded his assent.
Then the captain, in the bow, chuckled in a way that expressed humor, contempt, tragedy, all in one. "Do you think we've got much of a show, now, boys?" said he.
Whereupon the three were silent, save for a trifle of hemming and hawing. To express any particular optimism at this time they felt to be childish and stupid, but they all doubtless possessed this sense of the situation in their mind.
A third person point of view may be expressed as a limited point of view. This means that the narrator is limited to the thoughts, feelings and motives of one character and all perception and experience comes through that one character’s expressions, thoughts, feelings, and reactions. As you can tell from the quotation above, this clearly is not the exclusive case with the narrator in this story: the narrator witnesses and speaks for all the characters, even to the extent of seeing them sometimes as a unified group:
A young man thinks doggedly at such times. On the other hand, the ethics of their condition was decidedly against any open suggestion of hopelessness. So they were silent.
What does occur in this third-person limited omniscient point of view is that the narrator focuses greater and greater attention on filtering perceptions through the correspondent. This filtering focus is not so apparent in the beginning of the story but becomes more evident as the story progresses. It is foreshadowed in passages like this one in which the correspondent's perceptions are featured: "there was this comradeship that the correspondent, ... knew even at the time was the best." By the end of the story, the narrator limits the focus almost exclusively to the correspondent:
Then [the correspondent] saw the man who had been running and undressing, and undressing and running, come bounding into the water.