Earlier quoted context omitted.
I don't know about NY or Paris, but the comparison against London seems fair enough. They seem to be using a Tokyo metropolitan area of about 2000 km^2, and comparing it with Greater London at 1572 km^2. And indeed, people throughout Greater London are entirely used to living in small, damp, shared boxes.
The geography of the "cities" is very different though (look at the density of population maps provided), where "Tokyo Metropolitan" is one third pure mountains, then one third low-density living (think L.A.) and then one third what people normally thinks of the city of Tokyo, all of these in a sausage-like shape, while "Greater London" grows in a circle and so it's a circle-ish area. See this image with the labels,…
The real dense part that looks like the pictures of Tokyo you have most likely seen is around the Yamanote line, a train line that circles an area that is about 1/10 of the green area.