DFT study on the structural and electronic properties of the 2D π-conjugated poly -N=N- and -N=CH-linked 1,5-dioxocine and the planar van der Waals AA- and AB-stacked bulks and bilayers thereof is presented. According to electronic structure calculations with Heyd–Scuseria–Ernzerhof 06 (HSE06) density functional, the single polymer sheet is an indirect bandgap semiconductor (Egap=0.51 eV). However, under the lateral strain of + 6.00 % and + 3.75 % along the crystal lattice vectors a and b, respectively, it turns into a direct bandgap semiconductor (Egap=0.52 eV). The 2D polymer (2DP) aggregates feature interlayer distances in the range [2.86–3.65] Å. The AA-stacked bulk material has metallic conductivity, while other considered polymer aggregates are semiconductors with indirect electronic bandgaps in the range [0.14–0.49] eV. Charge carrier velocities in the studied systems are of the order of 105 m/s. The reported anisotropic optical absorption coefficient of the single polymer sheet matches well the corresponding electronic bandgap. The single 2DP and its aggregates may find applications in photovoltaics, (electro)photocatalysis, laser devices, (stretchable) electronics, and as a nano-sized conductors.