Use youtube-dl directly to download the video (thanks @meepybub!) Example:
youtube-dl -u <[email protected]> "https://vimeo.com/ondemand/<video>"
If variant 1 doesn't work, try this.
Login to Vimeo and get the cookies.txt file using this Chrome plugin
Use youtube-dl to download the video Example:
youtube-dl "https://vimeo.com/ondemand/<video>" --cookies cookies.txt
I had a lot of success with this repo for private videos: https://github.com/Tusko/vimeo-private-downloader
The linked extension no longer exists on the Chrome Web Store. I can confirm that Get cookies.txt works.