Should the forum functionality on an external site indent replies to original comments? The UI is different than the forum functionality on Verint forums.

I'll send you a video in DM Tom Paolucci  . We used the steps in this Verint article and then just updated the text to fit our needs:  How can I include forum behavior in an external website?  
Patrick M. it is embedded... I didn't know this was obsolete. What are the other options?

If its embedded then the UI will never be nested and is not customizable.  In fact embeddable forums are not actually meant to be treated like a forum as you can see in the UI.  They were a way in older versions to provide external commenting.   There are now several options to incorporate similar functionality from a pure REST perspective to a REST/widget solution using the scripted endpoint.  I highly recommend using one of these methods

Scripting REST Endpoints
REST API