I think this country is one of the few that this story would have worked best in. The concern with how the old will merge with the new is one a lot of people feel the pressure of, especially in a country as new as America. Having a war between the old gods and the new American ones was a good way to personify that struggle, especially since the new gods wants to do away with the old ones entirely.
Another way the story makes the old myths relevant is by making the gods be in hiding with the rest of us. In 'Percy Jackson' the gods can exist around humans, but often chose to only walk among them when its convenient. In 'American Gods' they have no choice, because they (or a part of them) were brought over when their believers migrated to the America, and now they are essentially stranded. They gain their power and worship how they can, through trickery usually.
Along with creating gods for modern sensibilities, 'American Gods' also uses the conflict of it's world to parallel current concerns and fears.