When the interactions between surfaces and adsorbates are studied, molecular rotations are often neglected. In this work, we carefully analyse the rotational dynamics of methane and ethane molecules desorbing from two different platinum surfaces by means of first-principles molecular dynamics simulations. With respect to its rotational symmetry, methane - a benchmark system for adsorption dynamics - constitutes a spherical top and ethane is a symmetric top. We focus upon the achiral Pt{110}-(1x2) surface, which exhibits both mirror symmetry and a stepped geometry, and upon the chiral Pt{531} surface, which exhibits kink sites and lacks reflection symmetry. For methane, neither a strong nor directed angular momentum is induced by either of the two surfaces, whereas for ethane we find an increased directionality for the molecular rotation upon desorption from Pt{531} compared to Pt{110}-(1x2). The principle of microscopic reversibility implies that such results (in time reversal) will also be relevant to the process of adsorption, which would therefore be sensitive to the initial rotational state of incoming molecules.