I don’t agree with the article and its definitions, it seems poorly sourced and to be advocating for English towns as the apex of civilization. That said, the photos provided and the descriptions focus more on the style of the buildings than urban form: “monotonous straight lines of modernist architecture” vs “historical architecture such as ‘Church’, ‘Castle’, ‘Tower’ and ‘Cottage’ made places look more attractive and get better ratings for their beauty.”
A "walkable" city has everything you need within walking distance. A "beautiful" city is devoid of modernist architectural monstrosities. A "lively" city is full of people.
I would argue there is no strong correlation here. A city can be walkable and ugly, lively and unwalkable, beautiful and unwalkable, beautiful but not lively...
When most people say walkable they mean safe to walk in. The trains don’t make it unsafe, and other than commuting you can do a fair amount using just walking or a bike because of the preponderance of small businesses that are safe to walk to. And you walk to and from the train station.
This is mostly meant to contrast to non-walkable spaces, where to walk to a store in an American suburb often means walking in a 3 ft wide path next to 55mph traffic and the crosswalks for said road are a half mile apart, if you’re lucky. The safe paths are circuitous if they exist and the pedestrian signals, if you can get a green one, may take minutes to cycle to and give you thirty seconds to cross 6+ lanes.
I think most people mean walkable to be more than maybe a half dozen square blocks of restaurants and small stores that aren’t really connected to anything else though. Bunch of examples in Silicon Valley.
Sure, bigger than a mall. The main point is that transit enhances walkability, they don't really compete in the absence of other factors (like transit in a highway median)