I believe she (and the Society) are wrong by following such reasoning. They keep on contradicting themselves. According to the latest Daniel-book (in my book p. 277) they refer to the Cold War, a covert war between the USSR, the King of the North, and the King of the South, the Anglo-American Empire. The Cold War started in 1948 and ended with the unification of Germany in 1990 (Dan. 11:40).
Interestingly, the next verse predicts the invasion of the land of the Decoration by the King of the North. Land of the Decoration they apply to their spiritual paradise (Dan. 11:41). So this King of the North is going to attack them. Contrary to expectation, the Communist King of the North has not disappeared. According to Daniel's prophecy, he is alive and well. Of this King of the North it is said "he will actually rule over the hidden treasures of the land of Egypt" (Dan. 11:43). Egypt in the Bible can refer to the world of mankind (cf. Rev. 11:8).
At its feet it will have Libyans (the Arabs) and the Cushites (black African nations). So this King of the North will make inroads in the world, gaining control over the world's commodities, especially oil. This world power will hold sway until its end (Dan 11:45). Even if interpretations may differ, this world power is not the King of the South, the Anglo-American world power. Personally, I view China/Russia as a likely candidate.