Children often mistake one word for another.
There is another somewhat famous novel called The World According to Garp by John Irving where a child mistakes the term undertow (at the beach) for undertoad, a toad that lives under the water.
undertoad and undertow
The word kite is not a derogatory term for a Jew. The child only knew the word kite so he didn't use the derogatory term at all. Only an adult who is familiar with the term will laugh precisely for that reason even though the term kike is very derogatory. It is the adult listener who substitutes the word given the rest of the phrase.
The idea that a Jew is kite, as understood by a child, is what creates the humor. Though one might say it is black humor, as the term one has to substitute is nasty.
This mishearing by kids is an example of a mondegreen:
One well-known example:
The national anthem of the United States is highly susceptible (especially for young grade-school students) to the creation of mondegreens, two in the first line. Francis Scott Key's "Star-Spangled Banner" begins with the line: "O say can you see, by the dawn's early light." This has been accidentally and deliberately misinterpreted as "Jose, can you see", another example of the Hobson-Jobson effect, countless times. The second half of the line has been misheard as well, as "by the donzerly light" or other variants. This has led to many people believing that "donzerly" is an authentic word.