Artículo de publicación ISI ; Context. The amount of molecular gas is a key to understanding the future star formation in a galaxy. Because H2 is difficult to observe directly in dense and cold clouds, tracers such as the CO molecule are used. However, at low metallicities especially, CO only traces the shielded interiors of the clouds. In this context, millimeter dust emission can be used as a tracer to unveil the total dense gas masses. However, the comparison of masses deduced from the continuum SIMBA 1.2 mm emission and virial masses (understood to trace the entire potential of the clouds) in a sample of giant molecular clouds in the Small Magellanic Cloud (SMC) by previous studies found a discrepancy between these two quantities that requires explanation. Aims. We attempt to more accurately assess possible uncertainties in the dust emission observed in the sample of giant molecular clouds from the SMC. We focus on the mass comparison in the densest parts of the giant molecular clouds where CO is detected to confirm the mass discrepancy previously observed. Methods. New observations of the southwest region of the SMC were obtained with the LABOCA camera on the APEX telescope. All the giant molecular clouds previously observed in CO are detected and their emission at 870 μm is compared to ancillary data. The different contributions to the sub-millimeter emission are estimated, as well as dust properties (temperatures, emissivities), to determine molecular cloud masses precisely. Results. The (sub-)millimeter emission observed in the giant molecular clouds in the southwest region of the SMC is dominated by dust emission, and masses are deduced for the part of each cloud where CO is detected and compared to the virial masses. The mass discrepancy between both methods is confirmed at 870 μm using the LABOCA observations: the virial masses are on average 4 times lower than the masses of dense gas inferred from dust emission, in contrast to what is observed for equivalent clouds in our Galaxy. Conclusions. At present, the origin of this mass discrepancy in the SMC remains unknown. The direct interpretation of this effect is that the CO linewidth used to compute virial masses do not measure the full velocity distribution of the gas. Geometrical effects and uncertainties in the dust properties are also discussed.