It could also stem from the fact the we properly refer to our country as The United Kingdom of Great Britain and Northern Ireland. Since Americans usually refer to “The UK”, perhaps the legislators thought that it meant NI was indeed a separate country.
Britain came into being with the union with Scotland in the early 18th C. Ireland (then the whole island) was added a century later, and Northern Ireland came into existence only in 1921 when The South became Eire.
This raises an interesting question - in principle, should a diversity visa programme be allocated by citizenship or by ethnicity? Should Australian aborigines be lumped in with other Australians? Should Russian Jews be considered on the same basis as other Russians?
There may be good pragmatic reasons why it is normally allocated by country of citizenship, but in principle diversity may be better served by having more (or fewer) Scots, Kurds, Xhosa, Bihari or Maya.
I don’t know. When you look at the list I posted above of the countries where the most visas were issued, it does appear that the program has achieved its goal of fostering diversity.