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Cellular appendages such as cilia and flagella represent universal tools enabling cells and microbes, among other essential functionalities, to propel themselves in diverse environments. In its planktonic, i.e., freely swimming, state the unicellular biflagellated microbe Chlamydomonas reinhardtii employs a periodic breaststroke-like flagellar beating to displace the surrounding fluid. Another flagella-mediated motility mode is observed for surface-associated Chlamydomonas cells, which glide along the surface by means of force transduction through an intraflagellar transport machinery. Experiments and statistical motility analysis demonstrate that this gliding motility enhances clustering and supports self-organization of Chlamydomonas populations. We employ Minkowski functionals to characterize the spatiotemporal organization of the surface-associated cell monolayer. We find that simulations based on a purely mechanistic approach cannot capture the observed nonrandom cell configurations. Quantitative agreement with experimental data, however, is achieved when considering a minimal cognitive model of the flagellar mechanosensing.