This randomized phase II trial studies how well cabozantinib-s-malate works compared with temozolomide or dacarbazine in treating patients with melanoma of the eye (ocular melanoma). Cabozantinib-s-malate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as temozolomide and dacarbazine, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. It is not yet known whether cabozantinib-s-malate works better than temozolomide or dacarbazine in treating patients with melanoma of the eye.