The foundation adopted it. Which is kind of my point.

No, there was no "X" prize that was adopted by the Nobel Foundation. They were offered a donation to fund the prize in the area of Economics, and they did. The prize itself has always been run by the Nobel Foundation.

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?