John, as far as I know it was simply Remington's in-house name for celluloid.
Edited to add excerpt from a Knife World article from 2000:
The early makers of celluloid handled knives used terms for their products like pyremite, pyralin, perfected stag, shell, pearl, ivoroy, composition and other names that they found suitable for the purpose of marketing. In looking through the catalogs, the word "celluloid" is avoided as much as possible. The reason appears to be the flammability issue. If you dissect the pyremite & pyralin terms used by Remington, you will discover the word "pyro," which means fire. I suspect that the public was not aware of this in the purchase of a knife with this type handle material.