When I click on my local subway stop it seems entirely accurate, and the stations don't form any kind of circle at all. In fact I can't find any subway stop origin that seems to form anything even close to a circle.
Also, according to the "about" it's calculating from actual subway schedules.
And it has nothing to do with street grids. It's subway trips, not walking.
The station-to-station part does indeed use subway travel times, but the website says "Hover over a station to see how much of the city is accessible within 40 minutes by subway and walking."
And the "walking" part clearly shows a perfect circle around each destination station, so it is 100% doing an as-the-pigeon-flies estimation for the walking.
"Isochrones are manually calculated using turf.js assuming 1.2m/s walking speed after the subway trip. These are simple buffers around each station/prior isochrone and do not take the street network into account."
Click on Rockaway park. A pigeon could reach those islands, but a walking person could not.
This is still a great visualization.
The site says "accessible within 40 minutes by subway and walking"