Orwell's Animal Farm meets the requirements of a fairy tale for several reasons. First, it contains many of the common fairy tale elements such as evil villains and noble characters. At first the villain appears to be Mr. Jones, but in the end the reader discovers that Napoleon is far worse. Boxer is the noble, hardworking, common character, who tries to defeat evil forces. He is willing to sacrifice his life if need be. Additionally, there is a castle of sorts--the farm--and royalty (Mr. Jones, who represents the Czar). One could also argue that the reader expects the story to end with the animals enjoying their freedom--a happily ever after ending--much like what the Russians originally expected when they threw off the reign of the Czar.
Secondly, the novellete is a beast fable which brings in the magical element found in fairy tales. Animals cannot only speak, walk around on two legs, and philosophize, but they also appear to be smarter than humans. The animals, not the humans, provide a moral (or lesson) at the end. This characteristic is common to beast fables, but it also works within a fairy tale because often animals or some other magical element provides the moral of the story.
Finally, and more specifically why Orwell describes his work as a fairy tale is because of his view of the Russian Revolution and the resulting rule of Stalin. Orwell sees the promises made by Lenin and Stalin to the commoners as being much like a fairy tale. They promised "happy endings" and a sort of utopia to the people, and yet they were the evil villains who stole happiness, equality, and success from their subjects. In Orwell's portrayal of Marxism, it is simply a fairy tale--something that sounds marvelous but is impractical and impossible to achieve.
The version of Animal Farm I am looking at calls it a fairy story rather than fairy tale, but I suppose it is the same. By my literature studies, I would be more apt to call it a fable- but who am I to argue with Orwell?
I believe it is like the Grimm fairy tales because it attempts to show a universal truth about the corruption of power. While the Grimms (as well as Perrault) usually focused on other themes, the fact that a universal truth is being presented in a fanciful manner tends to make it fall in lines with most definitions of a fairy tale.