In the "parallel novels" Desperation and The Regulators, the term "ini" crefers to a dimensional portal; in this case, a small aperture (only about an inch across in Desperation, and somewhat larger in The Regulators) that connects Earth to the dimension in which Tak was originally imprisoned by ancient forces unknown.
Despite its manifestation as a physical structure made of simple stone in Earth's dimension, the ini appeared to be magically incapable of being widened further to allow Tak's physical body to escape its extradimensional prison, since the various mining expeditions and demolitions made in China Pit over the years failed to ever widen the aperture, and since Tak never even attempted to have its can-tak and/or can-toi use the vast resources at its disposal to do so despite resenting its centuries of imprisonment there.
The term "ini" is phonologically similar to "thinny," a similar (if not the same) phenomenon seen in King's Dark Tower novels.