While this is a very simplistical and easy to rebuff argument as other replies did, a non-national "country" could be theoretically doable - save for the landmass, which is all occupied by existing ~national countries. Culture has not that much to do with national borders anymore. Just think about a "nation" of Elon Musk Followers, a nation of LGBTQ+ supporters, Real Madrid fans, or admirers of Oprah Winfrey.

Whenever we will be able to colonize landmasses like the Moon or Mars, it would be possible that these kind of artificial communities could flurish. Colonisation will most likely be done by market-driven corporations, which could allege with these communities based on donations/taxation.