@Nacho_Caballero The example you provided of an video that is unlisted, unlisted videos have different url structure.
And the way to embed unlisted video as per Vimeo request is different, ref Use oEmbed with private videos – Vimeo Help Center
I think a way around may be is to created your own embed using the doc above.
@sam
And for discourse, would it be better may be to use viemo API to get embed src url instaed of building it. ref https://stackoverflow.com/questions/51414260/vimeo-url-ive-never-seen-before-with-two-different-ids-how-do-i-get-it-to-work . And those lines releavnt discourse/lib/onebox/engine/vimeo_onebox.rb at 657256a099a601a0694d11d15c42ad76988efe8c · discourse/discourse · GitHub
Anyway if my specualtion is right then this should affect typical posting not only email: 1-Minute Audio Test for Stereo Speakers & Headphones-2ZrWHtvSog4