[jessaustin]

These parameters are not apparent to those with whom you share the shortlink, but I'd wager that the site stores a mapping from the shortlink to the session in which it was generated. Which may be OK for you; I don't know.

[Kliment]

the youtu.be link contains nothing but the video's identifier, so I don't see how they could store a mapping

[jessaustin]

Is the identifier unique? Does it have to be? Without switching to a different browser on a different IP addr and finding the same video again through a different search, would you even know?

[mintplant]

Yes, the format is youtu.be/<video id> where <video id> matches the one in the long URL (youtube.com/watch?v=<video id>&extra patameters...) and is unique to the video.