Western Rite is an SCA usage which means, broadly speaking, that the kingdom, person or custom under discussion originates in a kingdom originally descended from the West Kingdom. This is in contrast to Eastern Rite (or Eastern Orthodox) which refers in the same fashion to kingdoms descended from the East Kingdom. It is, obviously, a playful reference to the Western and Eastern Rite in the Catholic and Orthodox churches.
Sometimes the inhabitants are referred to as "the people of the Word" and "the people of the Book," a humourous reference to various religion's own self-reference. In the SCA it indicates that Kingdoms that spread out from the West tended to receive their culture via oral tradition whereas those who spread out from the East, were usually working from published documents provided by the SCA which often did not describe the reality of the SCA particularly well.
The "book" in question was probably the first edition of the Known World Handboke or possibly a forerunner of it entitled the Handbook of the Current Middle Ages, and the terms "People of the Word" and "People of the Book" were coined by Mistress Hilary of Serendip. (Probably.)