Testing the Addition of an Anti-cancer Immune Therapy Drug (Nivolumab) to the Usual Chemotherapy Treatment (Cisplatin or Carboplatin With Gemcitabine) for Recurrent or Metastatic Nasopharyngeal Cancer

Inclusion Criteria: * Pathologically (histologically or cytologically) proven diagnosis of NPC that has recurred at locoregional and/or distant sites. For locoregional recurrence, the disease must not be amenable to potentially curative surgery or re-irradiation. The following histological types are accepted: (a) Keratinizing - squamous cell carcinoma; (b) Non-keratinizing - undifferentiated or poorly differentiated * Measurable disease by the RECIST 1.1 criteria. Lesion(s) that have been irradiated previously can be counted as measurable as long as radiological progression has been demonstrated prior to enrollment * History/physical examination by a medical oncologist or clinical oncologist within 14 days prior to registration * Zubrod/Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 within 14 days prior to registration * Contrast enhanced magnetic resonance imaging (MRI) or computed tomography (CT) of the nasopharynx and neck within 30 days prior to registration * Contrast enhanced CT scan of the chest, abdomen, and pelvis within 30 days prior to registration * Absolute neutrophil count (ANC) \>= 1500 cells/mm\^3 (within 14 days prior to registration) * Platelets \>= 100,000 cells/mm\^3 (within 14 days prior to registration) * Hemoglobin \>= 9.0 g/dL (transfusion is accepted. Erythropoietin dependency not accepted) (within 14 days prior to registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) OR direct bilirubin =\< ULN for patients with …