IMO, if all you're looking to do is replicate what you see in the Unity demo, setting up an aim constraint in your native 3D program to control the head, neck and spine would probably be a lot easier than going into a game engine, setting up a similar constraint and then trying to get the data back onto a rig in your native 3D program. I would look at what's available in your 3D program first.
That said, if you do go the Unity route, I'm curious to hear what you learn. At a glance, it sounds like Unity supports FBX import and export, so I imagine this is doable. One of these days I'd like to look into it for its realtime render capabilities and possible game development, so any info on this topic is of interest to me.
Just curious but what is your native 3D program?
BTW, Animeeple also has a 'look at' type constrain. It's been awhile since I used this program though and I'm not sure the constraint affected the spine like the setup in the Unity demo; I
think 'Look_at_Block' only affects the head and neck. Setting it up is really simple to set up though. Go here for more info:
http://www.animeeple.com/documentation/Look_at_BlockHope this helps.
G.