You possibly have a virus infection. Viruses can be either present in the seed before sowing or injected into the growing plant later by various insects. In your case, given that you have some normal, if rather small, leaves first it looks like the latter case where the plant was visited by an insect which had previously been exposed to the sap of another plant, possibly a different species, which had the virus infection. You can read more about viruses in this PDF publication by the University of California.
It is unlikely that the plant can outgrow the infection, so the plant will eventually stop growing and dry up. In the meantime as it is visited by other insects the virus can be transferred yet again so probably the best thing would be to remove the plant and burn it. Given that the virus is in the area you might consider not growing watermelon there for a while. I'm sorry if this is a hard lesson for a beginning gardener. Maybe there is another location at some distance where the nephew can try again?