Role Application - is a parent containing element required?

Hi Folks,
In the Using ARIA documentation (https://www.w3.org/TR/using-aria/#using-application), it says that the role="application" should be placed on the "closest containing element" of your widget or widgets. 

I am specifically refering to the paragraph that says, 
"Put it on the closest containing element of your widget, for example, the parent div of your element that is your outer most widget element. If that outer div wraps only widgets that need the application interaction model, this will make sure focus mode is switched off once the user tabs out of this widget."

My question is it ok to place it on the interactive element itself? Or will not having a parent div affect how screen reader software manages focus mode when the user tabs off of the widget?

Here’s a code snippet that is working nicely:
<div tabindex="0" id="283-347-553-367" aria-label="‪Chemistry‬ book" role="application" aria-roledescription="move in four directions">‪Chemistry‬ book</div>
<!-- On-demand help text -->
<p description-283-347-553-367>Use arrow keys, or letter keys W, A, S, or D to move book or zoomed-in book up, left, down, or right.</p>

Note that we added an explicit aria-label to get all screen readers to read out the name of the widget.

Or is mark-up with an actual explicit application parent better? And  if so, how do we get an accessible name description read out. Would it be something like this:

<div id="283-347-553-367" role="application">‪
 <div tabindex=“0" aria-roledescription="move in four directions">Chemistry‬ book</div>
</div>

And I have a second question regarding multiple interactive widgets:
We actually have two interactive elements, a Chemistry book and a Zoomed-in Chemistry book, perhaps it would be better to have both interactive elements within the same div that has the role="application"? Currently, we are implementing them seperately, each with their own application role?

We are role=“application” for these interactive items because they can be dragged in 4 directions, and no native HTML elements or ARIA roles do that.

Any thoughts are much appreciated.
Taliesin Smith