From a quick read of the Nature article they posted:

These limiting assumptions were necessary based upon the urban scale scope of this study. Providing additional levels of detail at the building scale would greatly improve the accuracy of the analysis and can be refined in future works. Employing a cradle-to-cradle approach to consider resource reuse, the impact of retrofitting existing building stock over rebuilding; the inclusion of transportation impacts; adding a dynamic time component to investigate material inflows and outflows; and including a detailed time-related analysis of carbon sequestration potential offered by urban greeneries in the simulated environments—are all valuable and important avenues for future work to build on this study and expand its relevance while reducing its limitations. This study therefore acts as a stepping-stone to provide a strong foundation from which extensive future work can be born.

It doesn't even model transportation emissions, which kinda makes it worthless in the context of this discussion.

As for Spain, does Spain even have much "suburbia" as we understand it in a North American context? Data for cities in Spain may have nothing to say about the emissions of suburban sprawl vs denser communities, which is what the OP is mainly about.