I was wondering the same thing and was looking into it on a quiet Friday at work but then the afternoon got busy.
Best I could come up with is that the building has been there since the early WW1 era and given the ceiling layout and dimensions was likely a foundry and machine shop that was both ground and rail fed. All of the guns and mounts at Ft Tilden came from the Watervliet Arsenal, but once onsite all the maintenance and repairs would have required a good size foundry and works to keep all the batteries up and running, not to mention other duties on the Fort itself.
After the shore battery mission ended in 46 its likely most of the likely coal fired forges and steamworks (as indicated by the tall smokestack for such sandy ground) got decommed and scrapped and what remained got electrified. Clearly the building is pretty robustly built and has the structure to support internal cranes so undoubtedly when the Nike mission stood up it served as a warehouse supporting that and other post activities.
All of that could be totally wrong and is based on assumption of my own research, but thats my nickle less three pennies for what its worth.