Yes, I'm thinking that type of insulation and sleeving look original to me. (I'm old, so no guarantees.)
If you've got the time and the inclination to do so, It would be nice of you to sketch up a wiring diagram, and measure the resistances, and measure the amps or watts and write down fan and motor information: Blade diameter, Number of wings, anything that might help someone troubleshoot the fan. Put your name & date on your sketch, scan, or take a picture of it and submit as a .pdf file to Jamie Horner?? to add to my old wiring diagrams file...
Future fan guys will appreciate your efforts! I would give you a gold star right now, and a free wish on your favorite holiday!😇