Tokyo is relatively dense but it's nothing like what you expect from movies or from visiting there for a few days. The majority of people live in buildings 3 storeys or less (above 3 storeys there are a lot more requirements). There's a ton of detached houses even. The overall density of the 23 wards is slightly less than Paris.

When visiting you tend to visit some of the busiest areas and also spend a lot of time on the train. It's tiring and it seems so busy. But since almost every neighbourhood has all amenities and there is no single CBD, when you live there, you realise how much of Tokyo is an endless sea of small apartment buildings with small islands of restaurants and businesses around train stations, plus a handful of larger islands.

The article talks about the railways developing areas around Tokyo. This is actually very interesting and the way it sprawled[1] outwards towards places like Yokohama. Railways made commuter towns with amenities and commuter lines to those towns at the same time, and rented and sold real estate in those towns. Over time the areas in between the terminus of each of these lines (usually Shibuya or Shinjuku) and each town filled in until what you see today.

[1] I think the debate about whether or not Tokyo is/has urban sprawl depends on your definition. If you take it to mean expanding with lower density on the outskirts, it definitely "sprawled", although today it's more filled in. If you take it to mean unplanned low-density, car-centric expansion, it didn't "sprawl" that much. I've seen the terms car-centric sprawl and train-centric sprawl used to discuss the differences.