Projection mapping 3D objects on 2D surface

Hello,
I’m working on an interactive projection mapping game using Unity for my bachelor thesis (in software engineering), the concept resembles this one :

https://vimeo.com/32375248

I don’t know whether I should use a combination of Unity and a video mapping software, if there’s a free plugin already (I can’t afford the Omnity asset) or if I should do the projection mapping from scratch.

Any help would be much appreciated as I am new to this domain (projection mapping) and the documentation is pretty scarce.

PS: the projection mapping part shouldn’t be the focal point of my project (it shouldn’t take most of my time) as the game is already complex enough.

I’m not %100 sure, but maybe you should look into Augmented reality? It can project models and prefabs onto a real world surface. If you want everyone to be able to see it instead of just the person with the phone, try taking the game feed and putting into a projector.