I believe that in Spanish this is the common construction when you want to say that something is made of a certain material. They don't use "hacer" and instead say, in essence, the chair is of wood, or the book is of paper. In English though that is an odd construction, which is why we need to insert "made" in the translation.
I wrote "this chair is wood" and was marked wrong. However, I think that "of wood" though literal, is only appropriate under certain contexts.
Better would be "this chair is wood" or "this chair is wooden". Which is best depends, also, on the context. Probably at a furniture store, the clerk might readily say "this chair is wood.", and"wooden" would more likely sound strange.
It's common enough that it has hundreds of thousands of hits when "made" is included :/
I would agree that "is of wood" is technically correct in English, but it's not nearly as common, and the point of this sentence is to show that this is the Spanish method for describing what a material is made of. I think that's obscured if you accept it without the "made".