It seems to me to be an illusion, even a dream. Shige's house isn't that close to Kei's house. This cannot be possible, that a person with a physical disability could walk for miles.
Normally when they make mutual visits, they make the trip by car. And I would be surprised if he took a cab knowing that his mother keeps an eye on him all the time, besides the bad weather.
The weather situation. Kei's sudden exit, and the coincidence that Shuge shows up at his house at the same time. That is clearly a dream. <<DONTRYME, Shuzo>> è_é