The cosmic chemical enrichment as measured from damped Lyα absorbers (DLAs) will be underestimated if dusty and metal-rich absorbers have evaded identification. Here we report the discovery and present the spectroscopic observations of a quasar, KV-RQ 1500-0031, at z = 2.520 reddened by a likely dusty DLA at z = 2.428 and a strong Mg II absorber at z = 1.603. This quasar was identified as part of the KiDS-VIKING Red Quasar (KV-RQ) survey, specifically aimed at targeting dusty absorbers which may cause the background quasars to escape the optical selection of e.g. the Sloan Digital Sky Survey (SDSS) quasar sample. For the DLA we find an H I column density of logN(H I) = 21.2 ± 0.1 and a metallicity of [X/H] = - 0.90 ± 0.20 derived from an empirical relation based on the equivalent width of Si IIλ 1526. We observe a total visual extinction of AV = 0.16 mag induced by both absorbers. To put this case into context we compile a sample of 17 additional dusty (AV > 0.1 mag) DLAs toward quasars (QSO-DLAs) from the literature for which we characterize the overall properties, specifically in terms of H I column density, metallicity and dust properties. From this sample we also estimate a correction factor to the overall DLA metallicity budget as a function of the fractional contribution of dusty QSO-DLAs to the bulk of the known QSO-DLA population. We demonstrate that the dusty QSO-DLAs have high metal column densities (logN(H I) + [X/H]) and are more similar to gamma-ray burst (GRB)-selected DLAs (GRB-DLAs) than regular QSO-DLAs. We evaluate the effect of dust reddening in DLAs as well as illustrate how the induced color excess of the underlying quasars can be significant (up to 1 mag in various optical bands), even for low to moderate extinction values (AV ≲ 0.6 mag). Finally we discuss the direct and indirect implications of a significant dust bias in both QSO- and GRB-DLA samples. Based on photometric data from the KiDS and VIKING surveys and follow-up observations made with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, on the island of La Palma.