Recent progress in the on-surface synthesis and characterization of nanomaterials is facilitating the realization of new carbon allotropes, such as nanoporous graphenes, graphynes, and 2D π-conjugated polymers. One of the latest examples is the biphenylene network (BPN), which was recently fabricated on gold and characterized with atomic precision. This gapless 2D organic material presents uncommon metallic conduction, which could help develop innovative carbon-based electronics. Here, using first principles calculations and quantum transport simulations, we provide new insights into some fundamental properties of BPN, which are key for its further technological exploitation. We predict that BPN hosts an unprecedented spin-polarized multiradical ground state, which has important implications for the chemical reactivity of the 2D material under practical use conditions. The associated electronic band gap is highly sensitive to perturbations, as seen in finite temperature (300 K) molecular dynamics simulations, but the multiradical character remains stable. Furthermore, BPN is found to host in-plane anisotropic (spin-polarized) electrical transport, rooted in its intrinsic structural features, which suggests potential device functionality of interest for both nanoelectronics and spintronics.