I thought today the terms is used more generally, and could be used for a pulpy sort of plant substance too. Looking on dictionary.com we do have
1. the skin of sheep, goats, etc., prepared for use as a material on which to write.
2. a manuscript or document on such material.
3. a stiff, off-white paper resembling this material.
Still the last is clearly a derivative term. I guess I just wouldn't expect horses to be using the original sort.
Also on the wiki page you mentioned it has a section for additional uses of the term. It mentions that it's used to refer to graduation scrolls even though that's generally not classic parchment and has a section about "
Plant-based parchment" though it seems that term normally actually refers to baking parchment. However it also mentions vegetable parchment which is made of pulp and wood fibers. That looks like that may be for cooking too though. For some reason I thought there was a pulpy writing paper that still gets called parchment but I guess I was wrong there. Technically it can be plant based as we've seen, but not normally for writting, and can be used for non skins.. but pretty much just in a modern sense I guess... >_<