Under the Rules section there is the option for an App Catalog Rule. Within the App Catalog rule selection the option to add a Managed Google Play application. Within that pop up there is the option to select Managed Play which will open the iFrame into your Managed Play account. Note, this assumes you already have an Android Enterprise Binding associating your SOTI instance to a Managed Play account. You will need to do that first otherwise. From there you can approve applications for the enterprise and select them for the App Catalog rule. If it is an internal application you can use the Private App option to upload it into the iFrame.

With that said, I am not sure if Private apps support Managed Configurations or not. 

I'm not 100% sure either if Private apps support it either.  The android doc suggests it should be really easy to add custom code to the iframe to display the config options for the app.  This is the rabbit hole I've chosen :)

I suppose the part I'm missing before I can go further then is creating a binding association between Android Enterprise and our SOTI instance.  I just found the documentation for that and hopefully everything starts to fall in place once I do that and explore the new options I'll have under the Rules section you described.  Thanks.

The documentation for adding a Google Managed Enterprise to SOTI doesn't match my environment.  Is there perhaps an license to enable this feature?  Here's a picture of my environment and the documentation I was following:

There seems to be something wrong with your server installation.  If it is a MobiControl cloud server instance, open an official ticket with Soti support team to request a fix.  If it is an on-premises server, you have to check who is responsible for the installation and subsequent support/maintenance.