My take is countries do exist, but all of them gave up a certain amount of sovereignty for a world-wide government. In essence, you have the "United States of Earth," of sorts, and each nation is a state within the central world government.
So, it makes sense to me that two nations that so shaped world history still exist, just as Russia, France, Japan, and Brazil, other mentioned nations, do. It's just that by the 22nd century, those nations have learned to work together and formed a world government all nations are partnered in, rather than working alone and against each other. Basically, a utopia, where the UN actually works.