We present neutronics calculations for a hypothetical fusion reactor based on the repetitively pulsed concept of plasma-jet-driven magneto-inertial fusion (PJMIF). A PJMIF reactor is envisioned to have a replaceable, 3-m-radius spherical metal first wall exposed to 14.1-MeV neutrons; a fast-flowing FLiBe liquid blanket (with thickness 0.75 m) behind the first wall serving as the primary coolant and tritium-breeding medium; and finally an outer structural spherical wall shielded by the blanket. Cylindrical penetrations through both walls and the flowing blanket allow for hundreds of plasma gun drivers to inject hypersonic plasma jets that form both the deuterium-tritium plasma target and high-Z spherically imploding plasma liner to compress the target. This research is the first to conduct Monte Carlo N-Particle (MCNP6.2) and CINDER2008 neutronics calculations relevant to the PJMIF reactor configuration, with the primary objectives of determining (1) the neutron flux as a function of blanket thickness in the blanket and key reactor components and (2) the tritium production rate in the liquid blanket. These results will be used to estimate other quantities of interest, such as first-wall and gun-electrode lifetimes based on displacements per atom (dpa) accumulation, optimum blanket thickness, activation level of the outer wall and xenon liner, and achievable tritium-breeding ratios. Energy-dependent flux tallies were used to calculate neutron flux inside the FLiBe blanket and outer wall, as well as the cylindrical ports where plasma guns are located. Tally multipliers of the flux in MCNP6.2 estimated tritium breeding ratio, dpa, and nuclear heating, while the depletion code CINDER2008 was used to compare tritium breeding ratios with MCNP6.2 and calculate activation of the outer wall and xenon liner. These calculations provide a baseline for blanket requirements necessary for power production in a PJMIF reactor.