We present a first-principles investigation of the structural, electronic, and magnetic properties of pyrolusite (β-MnO2) using conventional and extended Hubbard-corrected density-functional theory (DFT+U and DFT+U+V). The onsite U and intersite V Hubbard parameters are computed using linear-response theory in the framework of density-functional perturbation theory. We show that while the inclusion of the onsite U is crucial to describe the localized nature of the Mn(3d) states, the intersite V is key to capture accurately the strong hybridization between neighboring Mn(3d) and O(2p) states. In this framework, we stabilize the simplified collinear antiferromagnetic (AFM) ordering (suggested by the Goodenough-Kanamori rule) that is commonly used as an approximation to the experimentally-observed noncollinear screw-type spiral magnetic ordering. A detailed investigation of the ferromagnetic and of other three collinear AFM spin configurations is also presented. The findings from Hubbard-corrected DFT are discussed using two kinds of Hubbard manifolds -- nonorthogonalized and orthogonalized atomic orbitals -- showing that special attention must be given to the choice of the Hubbard projectors, with orthogonalized manifolds providing more accurate results than nonorthogonalized ones within DFT+U+V. This work paves the way for future studies of complex transition-metal compounds containing strongly localized electrons in the presence of pronounced covalent interactions.