Apply jQuery events to all class elements?

Yes, it's possible. But you are using a jQuery selector (which can select and return multiple elements) and then immediately unwrapping it to return the first element. You can modify your code to use jQuery functions throughout and avoid this.

// an array of all elements with class "drag"
// each element is wrapped
var drag = $(".drag");

// selects all matching elements, but then references
// the first raw DOM element in the array
var drag = $(".drag")[0]; 

Another way of looking at it:

var matches = $(".drag");

// each() executes a function for each matched element
matches.each(function () {
    var drag = this; // raw dom element

    // or, wrap to get jQuery object
    // var drag = $(this);
});​

As I mentioned, you can also use jQuery functions throughout your code. Two quick examples I see are the x/y coordinate calculation and the event binding.

When you use $(selector)[0], you get the first DOM element that matches the selector. Use .each() instead to add the event listener to all elements that match the selector:

$(".drag").each(function () {
    var drag = this;
    xPos = drag.offsetWidth / 2;
    yPos = drag.offsetHeight / 2;
    drag.addEventListener("touchmove", function() {
        event.preventDefault();
        $(this).css({
          'left' : event.targetTouches[0].pageX - xPos + 'px', 
          'top' : event.targetTouches[0].pageY - yPos + 'px'
        });
    });
});​