The Near Shore is the full human world, but this game is based in Japan. And yes, it is modern-day Japan.

Normally speaking, the example you are giving would be the case. However, there are some residents of the Near Shore that are more acutely attuned to the Far Shore, such as animals (cats in particular) or babies. There are some instances, as well, of older people that have a hereditary ability to sense Far Shore residents more easily, such as Hiyori from the manga.