We investigate the electronic physics of layered Ni-based trichalcogenide NiPX3 (X=S, Se), a member of transition-metal trichalcogenides (TMTs) with the chemical formula, ABX3. These Ni-based TMTs distinguish themselves from other TMTs as their low energy electronic physics can be effectively described by the two eg d-orbitals. The major band kinematics is characterized by the unusal long-range effective hopping between two third nearest-neighbor (TNN) Ni sites in the two-dimensional Ni honeycomb lattice so that the Ni lattice can be equivalently viewed as four weakly coupled honeycomb sublattices. Within each sublattice, the electronic physics is described by a strongly correlated two-orbital graphene-type model that results in an antiferromagnetic (AFM) ground state near half filling. We show that the low energy physics in a paramagnetic state is determined by the eight Dirac cones which locate at K, K , K 2 and K 2 points in the first Brillouin zone with a strong AFM fluctuation between two K(K ) and K 2 ( K 2 ) Dirac cones and carrier doping can sufficiently suppress the long-range AFM order and allow other competing orders, such as superconductivity, to emerge. The material can be an ideal system to study many exotic phenomena emerged from strong electron-electron correlation, including a potential d ± id superconducting state at high temperature.arXiv:1811.02333v1 [cond-mat.str-el]