Hello, @arolnick!
Your question is a challenging one, only due to the clinical nature of it, so let me preface this with, "I'm not in any way qualified to speak on how immersive view can impact a therapy session, or how to make immersive view beneficial to a patient." That said, what I think I can help with is the technical aspect of this setup shown in the video you linked. The way to do this and make it appear as if two people are in the same space is fairly simple.
- You want to have your monitor offset from the camera, probably somewhere near 90 degrees. This will give the effect of two people facing each other.
- You will likely want the monitor at eye-level. One of the issues I saw in the video was the appearance that the gentleman on the right was looking into the chest of the man on the left. This was due to monitor height.
- Audio is often under-rated on importance here. The audio for both gentlemen in the video was not great. It can take you out of the head-space of being fully engaged in the conversation as the "muddy" sound can be distracting.
- One final consideration for this approach is the fact that it completely eliminated real eye-contact. What it did was gave the view of a third person, watching two other people speak, rather than the in-person engagement of eye contact.
I believe a simpler solution here is likely switching to Speaker view, so your own video view is eliminated. This will make it appear as if you are truly face to face, while eliminating the obvious boxes in Gallery view. Speaker view and full screen will go a long way for immersion in a one-on-one meeting. I hope this was helpful! Best of luck!