Clicking the doodle just redirects to a search, and under it it says "Upgrade to a modern browser and see what this doodle can really do." (pushing Google Chrome, of course.)
So I mess with my User Agent (Setting it to one for Firefox 12). It's still pushing Google Chrome, but otherwise the doodle works JUST FINE, and I can play music on it!
I even tested it with html5.enable set to the default "false" instead of "true" like I usually have it set, to see if that was it - nope, still worked just fine.
Why are they stopping the doodle from running on Firefox 3.6.x if it works just fine? Are they really that desperate to push their browser on people?