Rolex had a lower level sub-brand called 'Unicorn' back in the 1920's. I dont think they produced the movements for those sub-brands though as i understood they were sourced from wherever they could get their hands on them. You can read about the Rolex-Unicorn relationship here.
The photos are a bit fuzzy. Are there any markings other than the 'Swiss made' and "144" on the movement?