Characteristic of the "New Taiwanese Cinema" movement that Hou helped create, this scene is one of many in the film based on a long and continuous shot with gentle and continuous camera panning to follow the actor. The resulting effect is the feeling of watching the events of the film with what one might imagine to be a ghost's perspective on human interactions, matching the quiet and understated tone of the movie.
I love Three Times in much the same way that I love This American Life and Terrace House. All three have this"quietly aware" feel to them that I think is much more effective than most media in actually capturing reality.
Of the three in that group, though, I will say Hou's film stands out for its powerful visual aesthetic which is on full display here. The use of different colors of light is striking, of course, but so is the overall "playing in the ruins of Rome" feel that you get from watching Shu Qi pick up the abandoned florescent light—never dropping her cigarette!—and using it to illuminate the walls which seem to be overflowing with photographs.
Ira Glass and TAL alumni like Alex Blumberg talk about how TAL takes advantage of a lot of radio's core strengths; to me, Hou Hsiao-hsien is a master of cinema's core strengths, and this scene has really stuck with me because of how much comes together in it.