Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Third Person, Omniscient
You might think the narrative perspective of this story sounds very third person: the basic sentences and statements seem strictly factual, and we don't get a sense that the narrator has an opinion or bias. Or do we? It does seem that we have a bit more intimate connection with what's going on in the wife—more so than any other character. She's the one we travel with.
Our view of the hotel owner in particular is filtered through the wife's mind: Hemingway's perspective is more focused on what she feels and thinks about him than it is on the padrone himself. By staying in third person, Hemingway can also convey things about her that she might not be aware of in herself, like her feelings, which are described in a deeper way than she could articulate in speech. In this way, the narrator's omniscience (all-knowingness) allows Hemingway to both remain on the surface, above what characters may be thinking for themselves, but also to go much deeper than those personal conscious thoughts.