An improper use of NICS would be having personal info on an individual and being able to discover what types of guns the individual purchased. Say, for example, if they couldn't find any murder weapon, but then came along and said they were looking for a certain type of 9mm that the perp bought.
That doesn't seem to be the case here however, because they had the weapon. Once they have the weapon itself, it can be easily traced without using NICS or any other fed resources.
That's not NICS, it's really not any system, they call the manufacturer or importer, who is required to keep records of who they sell guns to. That wholesaler/distributor is then called. They provide the name of the dealer the gun was shipped to. They call, or probably in this case visit, the dealer, who looks in his records, which could include the 4473 form, and tells them who bought it and when.