Use youtube-dl directly to download the video (thanks @meepybub!) Example:
youtube-dl -u <youremailaddress@example.com> "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
I installed & used firefox's extension "Export cookies" when connected on the VOD page, then
youtube-dl https://vimeo.com/ondemand/xxxxxxxxx --cookies cookies-vimeo-com.txt
. The URL behing the VOD's one, which is the same as the trailer, but well when you're in the rental period it's the full video. It worked fine.