Event delegation without jQuery
The one thing different between your implementation and jquery.on is that jQuery allows you to bind on any element. One reason for that is performance. If on a deep tree, it would take a while for it to reach the delegate target. That's one reason jquery.live was deprecated.

Another is that your eventObject only accepts one callback per selector. If I were to register another callback under the same selector, then it would overwrite whatever was previously registered. Consider creating an array on the fly and push to it. You will need to change the way your code calls callbacks.