The term “cried himself out” is an idiom that means he cried until he could cry no more. He was very upset when he felt like the other boys abandoned him.
The boy wants desperately to fit in. He also wants to distance himself from his mother. He goes to explore a new area of the beach, one that is less safe, and finds some boys. They don’t want to play with him though, because he is a foreigner. When they frown at him, his heart sinks.
He knew the frown. At moments of failure, when he clowned to claim his mother’s attention, it was just this grave, embarrassed inspection that she rewarded him. (p. 3)
The boy’s reaction to the frown is very telling. He does not compare it to what other kids have reacted to him, so he must spend more time with his mother than with other kids. He desperately wants the companionship of kids his own age, and their appreciation. He also wants his mother’s.
He cried openly, fists in his eyes. There was no one to see him, and he cried himself out. (p. 3)
The boy feels alone, and abandoned. He thought that the other kids would want to hang out with him, and when he realizes they have left him he is miserable. He cries until he can’t cry any more.