That's a long list, but this book is crazy long, so it's not surprising that it incorporates a lot of different genres. We'll break it down into bite-sized pieces.
First up, dystopian literature. A dystopia (opposite of utopia) is a world where everything has gone wrong. The world of Atlas Shrugged certainly fits the bill. This book's plot tracks the course of an entire country's downfall, looking at the economic, political, social, and moral decline of a nation. We get all the hallmarks of a dystopia here: terrible and oppressive government, bad economic times, destructive philosophies (the looters), and the launch of a rebellion (Galt's strike).
Next up, mystery. The book starts off with a question: Who is John Galt? Like any good mystery, this book follows a number of overlapping and evolving mysteries. Just when one is solved, another one pops up. Questions lead to more questions and, though we get clues along the way, we are often left to ponder the various mysteries alongside our main, and very confused, characters.
A lot of the mysteries our main characters try to solve have to do with big ideas and philosophies, which brings us to our next genre. The book ambitiously seeks to lay out an entire philosophical system for us. We get to see Galt's philosophy and the philosophical errors of our heroes and antagonists in action. Throughout the book, characters are constantly delivering philosophical speeches.
The philosophy doesn't detract from the plot, though; on the contrary, it's a crucial part of it, sort of the umbrella genre here. Philosophy is at the heart of the dystopian ideas, the book's mysteries, and another major genre, the psychological thriller. Philosophy has to do with what people think, after all, which makes psychology a major part of the book. We get a lot of detail about our characters' states of mind, and particularly their stress levels as they try to solve various mysteries (hence the thriller part).
Characters try to solve all these mysteries and untangle all these philosophical puzzles, which also makes this book part of the quest genre. Galt's strike itself is a heroic and epic quest that spans the entire novel.
The last genre is science fiction, which might seem like a stretch – after all, it's not like there are aliens in the book. But we do have an alternate universe here that is more technologically advanced than the real America of the 1950s. So for instance we have technology like Galt's "heat shield," his "motor" that uses static electricity, the deadly sound waves of Project X, etc. These weird technologies add to the creepy atmosphere of the book and complement the other genres at work here.