Several bulk transition-metal dichalcogenides exhibit a strong optical anisotropy, high refractive index, and even a natural hyperbolic response, which are enabling ingredients in a variety of nanophotonic scenarios of great interest. Here, we investigate the electromagnetic response of NiTe2, a type-II Dirac semimetal, whose infrared/optical properties have been hitherto largely unexplored. Through density-functional-theory-based ab initio modeling, along with electron energy loss spectroscopy experiments, we show that NiTe2 exhibits a varied, extremely anisotropic response within the infrared and visible ranges. We also demonstrate the high tunability of its optical properties and illustrate the key role played by Dirac fermions. Our results pave the way for realizing nanophotonic devices for efficient light manipulation at subwavelength scales.