Javascript innerHTML is not getting updated

See the comments inline:

// Run when document is completely rendered and is ready to be manipulated 
document.addEventListener("DOMContentLoaded", function () {
    document.querySelector("#global-alert-queue .animate-in").innerHTML = "Change Text";
});

Demo: http://jsfiddle.net/tusharj/kg3cc4gw/3/

querySelector

Returns the first element within the document (using depth-first pre-order traversal of the document's nodes) that matches the specified group of selectors.

More on querySelector: https://developer.mozilla.org/en-US/docs/Web/API/Document/querySelector

seems like it is working correctly. Maybe you should move your script below the HTML. or check for document ready.

 var cls =document.getElementById("global-alert-queue").getElementsByClassName("animate-in")[0].innerHTML = "Change Text"; 

<div id="global-alert-queue" class="layout-wrapper">
<div class="alert success animate-in" role="alert">
Your submission was successful.
<button id="dismiss-alert" class="dismiss" type="button"></button>
</div>
</div>

You need to remove the var cls=.... Here's a working jsFiddle.

As per your updated requirement(Expected is "Change Text" should replace "Your submission was successful.")

You cannot update the inner html of animate-in as it will remove the button element also.

So one solution will be is to update only the first child of animate-in which is the text node containing the value like

document.querySelector("#global-alert-queue .animate-in").firstChild.nodeValue = "Change Text";

Another way is to update the markup to wrap the text in another element like

document.querySelector("#global-alert-queue .animate-in > span").innerHTML = "Change Text";

<div id="global-alert-queue" class="layout-wrapper">
  <div class="alert success animate-in" role="alert">
    <span>Your submission was successful.</span>
    <button id="dismiss-alert" class="dismiss" type="button"></button>
  </div>
</div>

you can add button as string with Text then you get your Output Demo Html

function changeText() {

  var cls = document.getElementById("global-alert-queue").getElementsByClassName("animate-in")[0].innerHTML = 'Change Text <button id="dismiss-alert" class="dismiss" type="button" onclick="changeText()">Change</button>';
}

<div id="global-alert-queue" class="layout-wrapper">
  <div class="alert success animate-in" role="alert">
    Your submission was successful.
    <button id="dismiss-alert" class="dismiss" type="button" onclick="changeText()">Change</button>
  </div>
</div>