Please explain how they are not theists. That's for my knowledge only. The statement "non-theistic satanists" is an oxymoron in my understanding. That's why I am asking you this question.
LaVeyan Satanism is a philosophy that uses Satanic and anti-Christian imagery for shock value.
When it was first created, it was based around the icon of Baphomet, who represents the God of Pantheism and could be interacted with through magic. As the Church of Satan grew in influence, its concept of magic became secularized to mentalism and it went from Pantheism to Naturalistic Pantheism to outright atheism.
During this change, many of the former members who were still theistic occultists left to form the First Satanic Church and the Temple of Set, which continued on the theistic traditions. Despite this, the Church of Satan continues to claim to be the only "true" form of Satanism, and rejects even other LaVeyan Satanists.
The actual philosophy, while loosely inspired by Crowley and Blavatsky's descriptions of the Left-Hand Path, is mostly taken from Social Darwinism.
LaVeyan Satanism used to be the most popular form of Satanism, but before LaVeyan Satanism there were the "Decadent" and "Symbolist" art movements that relied heavily on Satanic imagery inspired by Milton's Paradise Lost. These "Romantic Satanists" (as they came to be called) included figures like Baudelaire, Mary Shelley, Lord Byron, and Taxil. Being art, the use of Satanic themes was meant more as a critique of popular religious culture and an exploration of the taboo than literal devil worship.
This art movement inspired the current most popular secular Satanic philosophy, which is espoused by the Temple of Satan. The Temple of Satan pulls on the political philosophies of these Romantic Satanists, which are closely tied to socialism and anarchism.
There are Satanists who venerate Satan, which is sometimes called "Diabolism" or "Diabolatry" by LaVeyan Satanists to distinguish it from the secular philosophy, but they are more commonly known as "theistic Satanists." Technically, they predate both Romantic Satanism and LaVeyan Satanism, since they have ties to goetic demonolatry which traces all the way back to ancient Greece.