There are certain situations in which you don't need to notify parents about anything when treating a child--STIs are one of them. The reason being that untreated STIs will cause more spread as well as can lead to PID
The reason "do not prescribe antibiotics until testing results are available" is incorrect is because we already have a gram stain that shows gram-negative diplococci in pairs. This is Neisseria gonorrhoeae. So, no need to wait for test results come back.
The Q-stem stating that "Testing for Neisseria and Chlamydia" is ordered" after already having done the Gram stain seems to be a distractor.