Originally, rail worked kind of like this in the US too. Alternating squares of land adjacent to tracks were ceded to railroads, so you'd have sections of public land and private land beside each other.

I learned about this when someone was trying to make a test case of "corner crossing" from one patch of public land to another a while back.

You see the same thing in Hong Kong - the rail company practically creates new towns when they add a new station or extend a rail line.

I was under the impression Hong Kong was one big urban area already, is there really empty land new towns can be built on?

Yes. https://en.wikipedia.org/wiki/Hong_Kong#Geography, https://en.wikipedia.org/wiki/New_towns_of_Hong_Kong.

Most of the new territories is not highly developed. Kowloon and hk island are both entirely urban.

You can be smack in the middle of Central, and then walk up a path behind the Cathedral of the Immaculate Conception and be on Old Peak Road hiking up to Victoria Peak. Or be in Wan Chai, take the stairs next to the Rolls Royce car dealer, and be on Bowen Road Fitness Trail and in Aberdeen Park within minutes.

HK island, New Territories, the outer islands and even large parts of Kowloon are predominantly green, parks and forests.

As GP mentioned, occasionally the subway operator MTR will build a new station, build a shopping mall on top, and housing for 50,000 people.

A Georgist Land Value Tax would fix this!