The "redeemable in gold" language is on the back of that note.
One reason the "lawful money" definition eludes me is that these notes were redeemable for gold or lawful money. The notes appear to be in the nature of some sort of deposit certificate, making them useful to conduct transactions without actually handling whatever it was that was on deposit at the bank.
The constitutional limitation you point out runs to the states, and aimed to prevent paper monetization of debt by the states, which, although I'm not studied on the history, I think had occurred prior to the constitution being adopted.
Money is a strange and powerful thing. A convenience over barter, a tool to facilitate commerce large and small. It should be created in proportion to agricultural and industrial production (which isn't always production, people are paid to demolish things, too), and destroyed after it has served its purpose.
But, still getting back to basics, a "note" is a promise to pay, not currency. That promise to pay was repeated on the early FRNs, US Notes, and Gold and Silver Certificates.
That would seem to exclude paper as "money" and leave hard coin or bullion.