We present Monte Carlo computer simulations for melts of semiflexible randomly knotted and randomly concatenated ring polymers on the fcc lattice and in slit confinement. Through systematic variation of the slit width at fixed melt density, we first explore the influence of confinement on single-chain conformations and inter-chain interactions. We demonstrate that confinement makes chains globally larger and more elongated, while enhancing both contacts and knottedness propensities. As for multi-chain properties, we show that ring-ring contacts decrease with the confinement, yet neighbouring rings are more overlapped as confinement grows. These aspects are reflected on the decrease of the links formation between pairs of rings. The results suggest that confinement can be used to fine-tune the mechanical properties of the polymer network. In particular, confinement biases the synthesis of networks that are softer to mechanical stress. Finally, in connection with a previous study of us and recent simulations on two-dimensional polymer melts, our findings suggest that entanglements in polymer melts arise from pairwise ring-ring links alone.