I do like the retcon that "Cats aren't extinct". Since Fallout games tend to be localized affairs (nobody in California, Nevada, Massachusetts, or Maryland should really have any idea what's going on in Iowa or Oklahoma after the bombs fall, let alone across the ocean), the most any Fallout game can really say is "there are no cats here" not "there are no cats anywhere."
And the bombs hitting first on the West Coast (because it's closer to China) ought to give the East Coast some warning. ICBMs follow sub-orbital trajectories, and it takes about 90 minutes for something to orbit the earth at a sub-orbital trajectory, since the circumference of the earth is ~40,000 km and the distance from San Francisco to DC is ~4000 km, there should be something like 8 or 9 minutes of warning, assuming a simultaneous launch, and China is launching across the pacific instead of across the north pole (which is how a nuclear exchange with Russia would have went.)