"The book states that there's a theoretic component of man's existence which is primarily Western"

The book Pirsig refers to is The Meeting of East and West by American philosopher and teacher F.S.C. Northrop. It presents the thesis that an 'undifferentiated aesthetic continuum' exists in the East whereas Western thought is informed more via rationalism. This means that a concept in the East will be understood by intuition, while in the West it will be understood by postulation. This difference relates directly to Pirsig's Romantic and Classical understanding respectively.