I've got some ideas on how to accommodate this functionality. If the app is started being aware of GET arguments describing the play-list and the UTC timestamp when it was begun, it should be possible for a second browser to be started, calculate UTC difference, apply that to the playback time of the tracks in the play-list until it catches up with the initial arguments.
Of course, the sync can never be exact due to all the variances between endpoints, their access to accurate time, and all the other services between the two listeners with their individual web experiences. We can use UTC time as a common element and we DO know the play-time of each track thanks to the code.
Timing Chart:
User #1 sets a "ListenWithMe" flag on their session. When they hit the play button the app will offer them a copy-link to an URL which they can paste into any chat environment. The string they chat will include a href to others to "follow" them in playback.
User #2 sees the link in a chat session. Clicks it to launch a web-browser which pulls the arguments including UTC start time and the app will then attempt to load the play-list, check the time of each track, subtract time from the Now() until the UTC is relatively close. The release the playback to autoplay.