I think Chrome is able to do this because it separates tabs into processes, but I don't think there's a good way for Firefox to do it since everything is in a single process.
I don't think this has to do with multiprocess. The instance of HTML engine (geckk?) just needs to track who used the audio API.
I think the problem with that is it doesn't work with Flash audio. With multiprocess browsers, the Flash audio can be associated with a tab, but that's awkward/not possible if everything is in the same process.
Well, Chrome still often shares the same process for groups of tabs. I think this particular feature has something more to do with a change they made to their plugin API.
Chrome didn't have this feature for a very long time, and if anything sounded like it was actually harder because of how Chrome handles their processes.