“document.getElementByClass is not a function”

You probably meant document.getElementsByClassName() (and then grabbing the first item off the resulting node list):

var stopMusicExt = document.getElementsByClassName("stopButton")[0];

stopButton.onclick = function() {
    var ta = document.getElementsByClassName("stopButton")[0];
    document['player'].stopMusicExt(ta.value);
    ta.value = "";
};

You may still get the error

document.getElementsByClassName is not a function

in older browsers, though, in which case you can provide a fallback implementation if you need to support those older browsers.