Your citation is off, but the travel rule does require the transmission of "any other specific identifier of the recipient" (in addition to name and address) if it is received. To my knowledge there is no official interpretation or example.
From my perspective, it focuses only on information that would help in identifying the individual or the entity that is to receive the proceeds of the wire. Examples are difficult to come by, but a phone number might qualify. In simpler times (when this regulation was written), if the bank was sending a PUPID wire, it might have included the beneficiary's SSN, DL number or a portion of either. That's hard to imagine now.
A failure to include instructions requested by the originator; e.g. a reference to an invoice number, would be a customer service error, but would not be a violation of the travel rule.
If you want a more authoritative opinion, try the Helpline.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.