You are correct that this is not one of the original 1901 categories and was created by the Nobel Foundation upon receipt of a large donation/endowment from a Swiss Bank. While often referred to as the Nobel Prize in Economics, it's technically the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. It's granting is overseen by the Nobel Foundation as "one of it's own" using the same standards of impact as for chemistry, physics, or physiology/medicine.
en.wikipedia.org/wiki/Nobel_Memorial_Prize_in_Economic_Sciences (for anyone interested in the details).
I would, however, argue that over the past 45 years, the breadth of contributions recognized by the Economic Sciences committee has broadened beyond Hayek and Friedman. Many of the awards are much more technical in nature, dealing with understanding the structure of capital markets (Modigliani or Fama for example) with limited commentary on or implication for society. A lot of them (Sharpe for example) are really just high powered math applied to money/markets. The prize winners at LTCM (I think it was Merton and Scholes) got it for developing a method to price risk...and it worked great until real life got in the way. And my fav, Paul Krugman, certainly can't be lumped in with Friedman just because he's got a gold disk.
The reason I called it a Nobel Prize is that, for whatever the reason in 1969, the Nobel Foundation adopted Economic Sciences as one of it's own. 45 years later, I think it still recognizes "pretty damn good work" in the field. And besides, it's a lot easier that being a Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel Laureate.
So, I get your point and it's technically accurate but I think we've reached the days where the distinction is a nuance of perfection rather than a meaningful differentiation in communication.
As a fun aside, I worked with a guy who had dinner a couple years ago with Harry Markowitz - a guy who shared the 1990 prize for his theory on efficient portfolio construction that is at the heart of many asset management programs. His current attitude about the efficient frontier (his language for getting the right balance of risk vs. return) is "yeah - it was interesting for a while but I don't subscribe to it any more." Gotta love a guy who's not even practicing what he's known for.