Explaining Fogdancing requires us to dig deeper into Watchmen's world and its connections to the graphic novel. In 1985, the author of the book, Max Shea, is kidnapped by Veidt and used to create the alien squid that destroys New York. Once the plan is done, Shea is killed by Veidt, along with everyone involved. But before his death, Shea writes Fogdancing.
According to Peteypedia, the book is about the experiences of soldiers in Vietnam but told in a "fragmented, stream-of-consciousness prose" that makes readers feel "lonely, humbled and painfully mortal." Which fits Veidt's explanation to the Gamekeeper. The book is also deeply connected with masked heroes (The Comedian, Rorschach, Mothman, and even Dr. Manhattan had copies.)
It seems Veidt has been struggling to find his place in the world, and his trip to "paradise" has left him even more dissatisfied. Reading Fogdancing might be an outlet for his emotions.