The reason we can claim this story conversation, or dialogue, is about an abortion is because the American man gives a clue to the topic substance. He says, "It's just to let the air in."
"It's really an awfully simple operation, Jig," the man said. "It's not really an operation at all."
The girl looked at the ground the table legs rested on.
"I know you wouldn't mind it, Jig. It's really not anything. It's just to let the air in."
The girl did not say anything.
"I'll go with you and I'll stay with you all the time. They just let the air in and then it's all perfectly natural."
One of the types of procedures for abortions is called aspiration. The American man might simplistically understand it as letting "the air in." Of course, his understanding is simplistic and limited as is illustrated by his correlated remark that it's "not really an operation at all" and that Jig "wouldn't mind it." So it is very probable that the man understands the whole procedure in simplistic terms as letting "the air in."
Another clue is that later on in the story he says, "I don't want anybody but you. I don't want any one else. And I know it's perfectly simple." This allows us to infer that (1) if Jig does not do "it,"which is perfectly simple, they will no longer be alone; they will be more than "anybody but you"and the American man, and (2) that which will intrude upon just the two of them can be eliminated with the "perfectly simple" procedure that is "not really an operation at all."
These clues combine to paint the picture of an unplanned pregnancy and an upcoming--though still being debated and discussed--procedure to rid them of it. Though not an entirely true description, Hemingway reveals enough through the man's limited thoughts for us to piece the ideas together with a little detective work to arrive at an abortion as being the topic.