I'm not referencing the specific NY code, but even if it is amended from the model I-codes, this particular subject may not be. Here is the I-code answer:
The projection distance applies from the top of the handrail, down to the floor/treads. This means the handrail could be mounted to a wall and simply project out horizontally. This also means the handrail could be attached on top of a guard assembly, and the entire assembly below the guard can cut in to part of the required width. The minimum width must be maintained in the region above the handrail(s)
Consider the average human body. We are wider at our shoulders than our hips. We carry stuff in our arms. The stairs can be narrower between the handrails and to the ground than it can be above the handrails.