How to implement event-driven JavaScript without involving any DOM element?

Sure! The keyword you're looking for is "pubsub". Here are some well-known implementations:

• As a jQuery plugin
• PubSubJS
• EventEmitter2
• Backbone.Events

But you could also do it yourself, like so:

window.pubsub = (function () {
    var eventToListeners = {};

    return {
        sub: function (event, callback) {
            if (!eventToListeners.hasOwnProperty(event)) {
                eventToListeners[event] = [];
            }
            eventToListeners[event].push(callback);
        },
        pub: function (event, args) {
            if (eventToListeners.hasOwnProperty(event)) {
                for (var i = 0; i < eventToListeners[event].length; ++i) {
                   try {
                       eventToListeners[event][i].call(null, args);
                   } catch (e) {
                       if (console && console.error) {
                           console.error(e);
                       }
                   }
                }
            }
        }
    };
}());

// Sample usage:
pubsub.sub("arraySorted", function () {
    console.log("array was sorted");
});

var myArray = [2, 3, 1];

myArray.sort();
pubsub.pub("arraySorted");

In newish browsers, we've added the ability to construct an EventTarget directly:

const et = new EventTarget();

et.addEventListener("arraySorted", () => {
  console.log("array was sorted");
});

const myArray = [2, 3, 1];

myArray.sort();
et.dispatchEvent(new Event("arraySorted"));

See https://developer.mozilla.org/en-US/docs/Web/API/EventTarget/EventTarget for more examples as well as a browser compatibility table. As of the time of this writing it only works in Chrome (64+) and Firefox (59+), but over time support will expand to include Safari and Edge.

Mixing Backbone.Events into your object would give you this. (See Backbone.js)