The paper makes a strong distinction between money, credit, and cash without explaining the importance or relevance of the distinction.
The importance is implicit in the fact that it is an objective distinction, based on the properties of gold versus credit tokens.
Credit and cash are generally considered forms of money, so it seems to me that basing the paper on the fact that the three are different would require some explanation.
The paper tends to abuse the term "natural". It makes a big point about how money is naturally unique when a better description is "distinct".
Why is it better? The term "natural" is used because credit tokens are artificial or man-made; they cannot be found naturally like pieces of gold or valid nonces. Why is this not important in your view?
I believe the point being made is that the importance of a "naturally unique" item is that it cannot be duplicated. But, "naturally unique" does not depend on it being "natural". There are "natural" things that cannot be "naturally unique", such as the color blue. The term "tangible" comes to mind, but it is also limited. I think "distinct" is the term that precisely describes the property you are describing.
The paper conflates a chain of blocks with a chain of transactions.
A chain of (transaction) blocks is a chain of transactions.
A chain of blocks
contains chains of transactions, but they are not the same. The links between the blocks are not the same as the links between transactions.