On one page of the story the American says, not once but three times, that Jig doesn't have to go through with the operation if she doesn't want to.
"Well," the man said, "if you don't want to you don't have to. I wouldn't have you do it if you didn't want to."
"I think it's the best thing to do. But I don't want you to do it if you don't really want to."
"I don't want you to do it if you feel that way."
Then on the last page:
"You've got to realize," he said, "that I don't want you to do it if you don't want to. I'm perfectly willing to go through with it if it means anything to you."
"But I don't want you to," he said. "I don't care anything about it."
That's five times in a very short story that the man says she can have the baby if she really wants it. He obviously, though reluctantly, is saying that he is willing to support her and the baby, which seems to mean that he would give up the nomadic, irresponsible life they have been leading, get a job, and become the breadwinner. She wouldn't consider having the baby unless they were married. Maybe young women have different views now, but they didn't in the 1920's. Since he is an American, he would very likely have to move back to America. He doesn't say that they would get married, and the fact that neither of them mentions marriage makes me think they are married already.
Jig is apparently not an American. If she moved to America with the man, she would have to be married to him in order to stay in the country. Maybe she couldn't even get into the country unless she was married to an American.