Once the internet goes down it goes down, and you'd have the local cached copy.

I'd also have this mystical device print out the entire website in paper form every year or so, and then it would automatically shove the book version of it in a miniature Warehouse.

I don't think electronics are going to function any way similar to they do now in 200 years. But books, particularly picture books will always be readable. We already have examples of this, hieroglyphics are thousands of years old but can still be read and interpreted by modern people even without knowledge of the language they were written in.