As no character is telling the story him/herself, this is 3rd person point of view. Fitzgerald cheats a little, though. A story in 3rd person should either be limited - through the eyes of a single character - or omniscient - through the eyes of multiple characters. Fitzgerald does both.
He mainly uses limited, gearing the narrative through Charlie's perspective. Everything that happens is portrayed as Charlie sees it, allowing the audience to both be removed from Charlie, but exposed to his "vision". Since the conflict is Charlie's and is very personal (dealing with grief), this choice of point of view makes sense. Here is an example:
- "He would come back some day; they couldn't make him pay forever. But he wanted his child, and nothing was much good now, beside that fact.... He was absolutely sure Helen wouldn't have wanted him to be so alone."
In the above passage, it is Charlie's hopes and plans that the audience hears. In contrast, here is an example of Fitzgerald breaking the rules and letting in another character's perspective:
- "...part of her [Marion] saw that Charlie's feet were planted on the earth now, and her own maternal feeling recognized the naturalness of his desire;"
This occasional break from the technique allows readers momentary glimpses into how Charlie is viewed by others, broadening our understanding of the protagonist.