The redemption of the Gentiles will come according to the degree to which they accept the newly revealed truth, the new restoration of those plain and precious parts of the gospel which have been lost. As the Gentiles accept this new restoration, they become numbered with the house of Israel and receive the blessings which are promised to the house of Israel. The second promise to the Gentiles is that they will be preserved from captivity.
There are two ways to read this prophecy. The first is to assume that captivity refers to the condition of the Gentiles before coming to North America. If we read that, then the promise of freedom from captivity would apply to a location, and perhaps a government. That might refer to the governments of North America, but would appear to exclude much of the world's population from these benefits.
Another reading is that the captivity is not that of mortals, but of the image of the great and abominable church. Under this reading the captivity would be spiritual, and the freedom from that kind of captivity is open to all who accept the gospel, in any land, despite the nature of their government. This reading appears to fit better with the context of the great and abominable church theme which is about to resume, and with the known impact of the gospel on the modern world.