Creating a Underground camera like Game of Dwarves?

So i got a quick question, not necessarily how to do it, but more pointing me in the right direction because I don’t really know what this type of setup would be called.

For those not familiar with the Game of Dwarves underground building it looks like this

http://media.pcgamer.com/files/2012/01/A-Game-of-Dwarves-5.jpg

Skip to 10:30 if you want to see what i mean by their digging/queue setup…

I am looking to make a unrelated game that has underground digging, and i think that the way they have everything setup is ideal for the game i am looking at doing.

But i have no idea what or how they are doing it, do they just have a big underground set of voxels? The way the camera works and “see’s through” the ground and you select blocks seems like a total mystery to me. I cant wrap my head around how voxels would be how it works…

If anyones got any ideas how they accomplish it, that’d help me a ton in at least knowing what i need to research.

One trick I’m using in my game that I’ve noticed in those screenshots: walls are simple one-sided planes. That way, walls will be invisible or visible based on direction camera is looking at. Just make the wall plane face the corridors. Other decorations, like support beams, are solid objects that will be visible from all sides.