Is Paris 6 times smaller than Madrid and 15 times smaller than London? Seems suspicious to me. What exactly is the boundary of this "area" and how does it relate to the subway network?

A significant proportion of the administrative area of Madrid is covered by fenced-off forests. Plus it covers other swathes of non-developed land and even most of its airport. The administrative area of Paris proper, on the other hand, is fully urbanised. See here for comparison:

+ Madrid: https://www.openstreetmap.org/relation/5326784

+ Paris: https://www.openstreetmap.org/relation/7444

London is a whole different animal. While Madrid and Paris are arguably "similar" cities in terms of urban design and residential density, London and UK cities in general are completely different.