At some point, decades prior to construction, the road would have been vacated and either became a stand-alone parcel or (more likely) became part of the parcel directly to the east. You can probably assume that a fairly important/large building was there in the late 1800s. If the road still existed when the Chrysler Building was being planned, you would assume that NYC would have vacated it and made it part of that…
It’s reflected in three properties on that block, the Chrysler building itself and its neighbors (it's BBL 1297-23, 1297-27 and 1297-33). Oddly it only shows up on that block, blocks to the north and south don't show the outline of the road.
Not sure if this will link correctly: https://propertyinformationportal.nyc.gov/parcels/parcel/101...