This story is written from a third-person omniscient point of view. The narrator knows Jerry's mother's thoughts and feelings. For example, the narrator says, early on, that "She frowned, conscientiously worrying over what amusements he might secretly be longing for which she had been too busy or too careless to imagine." Thus, the narrator can tell us what specifically Jerry's mother is thinking about and that it makes her anxious for her son's well-being.
The narrator also knows Jerry's thoughts and feelings. Shortly after the description of his mother, above, the narrator says, "[Jerry] was very familiar with that anxious, apologetic smile. Contrition sent him running after her." Thus, the narrator can tell us that Jerry knows his mother's concerns well and that he feels guilty for making her worry.
Further, the narrator knows the thoughts and feelings of the older boys who come to play at the wild bay. Although the narrator doesn't belabor this, he does say that "they understood that [Jerry] was a foreigner strayed from his own beach, and they proceeded to forget him." Therefore, the narrator knows the thoughts and feelings of all of the characters in this story, and this means the narrator uses a third person omniscient point of view. He is not a participant in the story (this correlates to the third person) and he knows the thoughts and feelings of all characters (omniscient).