Not all touch device browsers/apps support the click event because it is a mouse event. Why don't you try using Sencha's normalized event system to bind a click handler to the component, you can then check if the <li/> was clicked inside the component's click event handler.
Sencha has already done the work for us so we can handle clicks & taps in the same manner, so take advantage of it.
Btw, event delegation from a parent element is usually more performant than binding event handlers to a bunch of different DOM elements. It looks like your binding events to elements in a loop, this is a bad practice. I just wanted to point that out too.
Here is a code example:
var cmp = Ext.getCmp('someComponentId');
cmp.on('click', function(me, event) {
if (event.currentTarget.tagName == "LI") {
// do something since the <li/> tag was clicked.
// event.currentTarget will be the <li/> DOM element,
// feel free to do with it as you please :)
}
}