This is an excellent question because the point of view shifts. Initially, the point of view of "The Open Boat" is told from the point of view of a third person narrator. This third person point of view comes from an objective vantage point, from one ostensibly not in the boat or not a character in the story. 

The perspective shifts to each of the four men at different times but definitely focuses mostly on the perspective of the correspondent. What complicates this shifting is that there are times when it is not clear which character's perspective is being presented. At times during dialogue, the reader is also unable to decipher who is speaking. This is all to underscore what the objective (removed) narrator described as the "subtle brotherhood" at the beginning of Part III. In other words, the shifting narration and lack of clarity about who is speaking highlights the fact that they are all in the same predicament. While each character is surely thinking different thoughts, they all act together out of an instinct of survival and a necessary camaraderie. 

And although the third person narrator is objective, he/she is not omniscient. This leaves the reader, like the narrator and the other characters, to guess and interpret what this shipwrecked experience must be like. In Part I, the objective narrator is not making statements with all knowing power. He/she is making assumptions about what the men might be feeling. 

In the wan light, the faces of the men must have been gray. Their eyes must have glinted in strange ways as they glazed steadily astern. Viewed from a balcony, the whole thing would doubtlessly have been weirdly picturesque. 

Note the verbs used: "must have been." The objective, third person is only relatively sure about the "balcony" view, stating that this view would "doubtlessly" have been picturesque. 

Crane wrote this based upon a real experience. Clearly, the correspondent is based on Crane. This is why, of all the characters, the reader gets most personal insight and direct perspectives from the correspondent. 

Also, there are instances where the third person, objective narrator shifts the perspective to all the men as a group. And this narration is what the third person narrator assumes. 

As for the reflections of the men, there was a great deal of rage in them. Perchance they might be formulated thus: "If I am going to be drowned--if I am going to be drowned--if I am going to be drowned, why in the name of the seven mad gods who rule the sea, was I allowed to come thus far and contemplate sand and trees? 

Note that the phrase "if I am going to be drowned" occurs three (not four) times. This shows a possible connection between the third person narrator and the correspondent. Since the story is based on Crane's own experience as a correspondent on a dingy following a ship sinking, this is logical. In this quote, the third person narrator supposes what each man might be thinking, with a possible nod to the perspective of the correspondent (or, less likely, to another character). 

Note: The point of view in terms of the narrator in this story is always third person. But, the point of view in terms of perspective shifts to the correspondent and, less frequently, to the other men. The narration only becomes first person (using "I") when the third person narrator supposes what the men might be thinking: as illustrated in that last block quote.