Hi Erik --
The sessionless launch URLs actually point back to Canvas rather than to the LTI tool, and then Canvas generates the regular LTI 1.1 POST request that launches the tool. Canvas uses the "verifier" token to look up all of the user and context information that would otherwise have been found in the session for a normal LTI launch.
An interaction diagram of the process might look something like this:

This is quite similar to what happens when a user clicks on a link to an LTI tool that appears in course navigation:

It's important to note that the sessionless launch URL bypasses Canvas authentication, and while it can only be used once it does allow the user to launch the tool as whoever generated the link in the first place.
Hope this helps! (I'm also interested to hear what others have to say about use cases!)
--Colin