They used to have the slang term "dick smithing" to describe what the American is doing inside the saloon. Typically a man might go into the kitchen to mix drinks for himself, his wife, and their guests. He would pour out the drinks and then pour himself an extra jigger of gin or whiskey and dick smith it straight down. It is obviously a kind of selfishness. There might be several reasons why the American dick smiths an extra Anis del Toro before rejoining the pregnant girl outside. He may just want to avoid renewing a conversation which threatens to turn unpleasant. He may feel that she had already had enough to drink, especially since she is pregnant. They have each drunk two large beers and one Anis del Toro. It seems pretty obvious that she shouldn't be drinking any more in her condition. But as far as the man is concerned, he may feel he needs an extra drink. He is a bundle of nerves. The girl is giving him a hard time. He has all kinds of logistical problems to deal with--and he has to do so in a foreign language. He will have to find a hotel, then make contact with an abortionist. He may only have a name or an address. Madrid is a big city. He will have to get the girl to the abortionist and then back to the hotel where he will have to take care of her while she recovers and in the meantime be hoping and praying that there will be no complications. He is breaking the law. He could get thrown in a Spanish prison. What if she dies??? He has no idea how this operation will affect his relationship with the girl. He is trying to be more patient, understanding, affectionate, and competent than he really feels. He delays in going outside to rejoin the pregnant girl because she only makes him feel guilty and anxious. Their conversations are going nowhere because of the huge, black problem hanging over their heads.
The importance of this is that she asked him to come back after leaving the baggage. But he is not coming back, he wants her to get an abortion because he is no longer interested in her and does not want to spend his life with her. Him going and having his own drink symbolizes how he is already planning on leaving her.