There is no Nobel Prize in Economics. There's only the "Nobel Memorial Prize in Economic Sciences" which was established in 1968 by a donation from Sweden's central bank.
It may not have been one of the original Nobel Prizes, but everyone who matters, including the prize-issuing organization itself, considers it to be one of the current Nobel Prizes. This is no different from, say, the Olympics--would you not consider snowboarding, boxing, weightlifting, wrestling, or volleyball (to name some of the most popular current events) to be Olympic events simply because they were not part of the first games in 1896? Conversely, should croquet and tug-of-war be considered Olympic sports even though they haven't been part of the games for over a century?