I've run into the same problem on Hatteras Island. I'm not sure there is a game store. Kitty Hawk Kites on the north end of Avon has the best selection of games that I've found. My suggestion is to check out the branch in Nags Head.
Less than 100 miles away are the Go! store in the MacArthur Center in downtown Norfolk and Tower of Games in Chesapeake.
The MacArthur store is gone. Tower of Games is pretty good.