It seems to me that the dictionary defnition of "animalism" has very little to do with the way Orwell is using the word. In "Animal Farm," "animalism" is a specific ideology that is pro-animal and anti-human.
The way that Old Major sums the ideology up is “All men are enemies. All animals are comrades.”
According to Old Major, animals must realize that they are better than people and they must, therefore, never act like people. They must not act like people in little ways (sleeping in beds) but more importantly, they must not act like people in big ways (acting like tyrants over others).
So -- animalism is an ideology (meant to stand for communism in real life). This ideology, and the way it is or is not carried out faithfully, is one of the main themes of the book.
The term 'animalism' has one definition in The American Heritage Dictionary of the English language Fourth Edition Copyright 2009 by the Houghton Miffin Company. It relates to the enjoyment of physical health and vigorous drives,but crucially, being indifferent to all BUT those physical appetites. It leads to the theory put forward by some that humans are no more than animals and have no spirtiuality. I hope this helps out in your requirements for illumination on the themes in the novel 'Animal Farm' by George Orwell. I have cited this source in the link below. There are also other descriptions and sources you can cite which may match your requirements more closely.See also the resources and sources on 'Animal Farm' by George Orwell on enotes.
Animalism is an allegorical mirror of the Soviet Union, particularly between the 1910s and the 1940s, as well as the evolution of the view of the Russian revolutionaries and government of how to practice it. It is invented by the highly respected pig Old Major. The pigs Snowball, Napoleon, and Squealer adapt Old Major's ideas into an actual philosophy, which they formally name Animalism. Soon after, Napoleon and Squealer indulge in the vices of humans (drinking alcohol, sleeping in beds, trading). Squealer is employed to alter the Seven Commandments to account for his humanization, which represents the Soviet government's tweaking of communist theory to make it more a reformation of capitalism than a replacement.
The Seven Commandments are laws that were supposed to keep order and ensure elementary Animalism within Animal Farm. The Seven Commandments were designed to unite theanimals together against the humans and prevent animals from following the humans' evil habits. Since not all of the animals can remember them, they are boiled down into one basic statement: "Four legs good, two legs bad!" (with wings counting as legs for this purpose, Snowball arguing that wings count as legs as they are objects of propulsion rather than manipulation), which the sheep constantly repeat, distracting the crowd from the lies of the pigs. The original commandments were:
- Whatever goes upon two legs is an enemy
- Whatever goes upon four legs, or has wings, is a friend.
- No animal shall wear clothes.
- No animal shall sleep in a bed.
- No animal shall drink alcohol.
- No animal shall kill any other animal.
- All animals are equal.
Later, Napoleon and his pigs are corrupted by the absolute power they hold over the farm. To maintain their popularity with the other animals, Squealer secretly paints additions to some commandments to benefit the pigs while keeping them free of accusations of breaking the laws (such as "No animal shall drink alcohol" having "to excess" appended to it and "No animal shall sleep in a bed" with "with sheets" added to it). Eventually the laws are replaced with "All animals are equal, but some animals are more equal than others", and "Four legs good, two legs better!" as the pigs become more human.