Step 1: The clinical clue is purulent urethral discharge in a male together with a microscopy finding of intracytoplasmic gram negative cocci, that is, gram negative diplococci inside neutrophils.
Step 2: Neisseria gonorrhoeae is a gram negative diplococcus that is classically seen inside polymorphonuclear leukocytes (intracytoplasmic). Acute urethritis with a purulent discharge is its most common presentation. This combination is essentially diagnostic of gonorrhea.
Step 3: The distractors do not fit. Donovanosis (Klebsiella granulomatis) shows intracellular Donovan bodies in tissue smears, not urethral diplococci. Bacterial vaginosis is a vaginal condition with clue cells, not a male urethral discharge. Syphilis is caused by Treponema pallidum, a spirochete, and presents with a painless chancre.
Step 4: The intracellular gram negative cocci with purulent urethral discharge therefore point to gonorrhea.