There's significant truth to this.
But it's all thrown off by his key storyline, which is this: The ancestors of white America came here as Protestant dissenters. They rebelled against religious authority. Built a society based around a strong work ethic and so forth. Romney and Ryan were basically in this tradition. And "these economic values played well in places with a lot of Protestant dissenters and their cultural heirs."
This is wrong. The folks he's talking about -- mainly settled New England and what we now call the Northeast. Their descendants by and large settled the upper midwest and the northern tier of the country. The map of settlement gets a bit more complicated when you get out beyond the Rocky Mountains.
You need only look at a map to see that these were the areas where Romney's economic values didn't seem to play well at all. Romney lost this zone almost on almost every count. If you're talking about the protestant dissenters who made up the early settlement of America, Romney didn't win their descendants. Nothing could be clearer.
They played well in the parts of America founded out of the hearth lands of the American South. The Carolinas, Georgia, Virginia, which spawned much of the Southern tier of the US -- again, roughly out to the Rockies, or out past Texas. This is the part of the country where an ingrained suspicion of and hostility toward government has always been most pronounced -- and where religious dissent as a reason for settlement was much, much less in play. That's partly tied to the history of slavery, though it's not reducible to it. It's also rooted in heavy Scots-Irish settlement which brought with it its own deep resistance to governmental authority. This is the cultural ethos of the South, with a related but distinct western permutation.
This isn't a matter of new groups bringing in some new set of economic values. That's really demonstrably wrong. America is a complex place. Ideological and cultural spaces are complicated. But we can identify broad cultural strains emerging out of early north and south of the country -- ones with significantly different mores, culture, openness to different ideologies.
To the extent these new groups have bought into the view of government and opportunity Brooks describes (a simplification but not too far off the mark), this isn't some new thing America or the GOP needs to adapt to. These are simply the economic values of the North. They're economic values the GOP was founded on. But the Republican party, roughly half a century ago, reestablished itself with that other tradition, that of the South. With these changes in the demographic complexion of America, that's an increasingly tenuous position.