Dense packings of semi-flexible polymer chains are researched through the Monte Carlo suite Simu-D [1] in extremely confined monolayers, effectively corresponding to two-dimensional films [2]. We systematically study the effect of chain stiffness on the packing ability and the emergence of local and global orders of semi-flexible polymers, modelled as linear chains of tangent hard spheres, the chain stiffness of which is tuned by a harmonic bending potential [3]. Thus, the limit of random close packing (RCP) is explored as a function of the equilibrium bending angle, while the local and global order of the emergent structures is quantified by the degree of crystallinity [4] and the nematic and tetratic orientational order parameters [5], respectively. A multi-scale wealth of structural behaviour is observed for the different semi-flexible systems studied, which is inherently absent in packings of athermal individual monomers, and which is surprisingly richer than that in three dimensions under bulk conditions. As a general trend, an isotropic to nematic transition is observed at sufficiently high surface coverages. As surface coverage further increases, the nematic phase is followed by the establishment of a tetratic state, which in turn marks the onset of RCP. For chains with right-angle bonds, the incompatibility of the imposed bending angle with the neighbour geometry of the triangular crystal (the densest structure in two dimensions) leads to a singular intra- and inter-polymer tiling pattern made of squares and triangles. The present study could serve as a step towards the design of hard colloidal polymers with tuneable behaviour for 2D applications. [1] M. Herranz et al., Int. J. Mol. Sci. 22, 12464 (2021). [2] C. Pedrosa et al., J. Chem.Phys. 158, 164502 (2023). [3] D. Martínez-Fernández et al., Polymers 15, 551 (2023). [4] P. Ramos et al., Crystals 10, 1008 (2020). [5] D. Andrienko, J. Mol. Liq. 267, 520-541 (2018).