It's a precision production lathe. The sticky out rods at the back are depth stops. A sequence of pre-set operations are applied to the same workpiece and the lathe was probably only one of several different machines on a production line that produced the finished item.
Watchmaking is a possibility but my guess is almost anything in the instrumentation line. D'Arsonval meter movements, gas & electricity meters, rev counter, telegraphic, barometer, navigational, dial caliper movement, dial pressure gauge, range finder, etc etc. I think it's too small for gunmaking.
Whilst wonderful for repetition work because they leave manual lathes in the dust, it looks too specialised for comfy general purpose machining.
Dave