(I’m not a Teardown dev!)
I tried this on a local project. It looks very jank and the math falls apart quickly. Unfortunately, using a fixed axis-aligned grid for rotating reference frames is not practical.
One to thing I wanted to try but didn’t, was to use dynamic axes. So once an entity is created (that is, a group of voxels not attached to the world grid), it gets its own grid that can rotate relative to the world grid. The challenge would be collision detection between two unaligned grids of voxels. Converting the group to a mesh, like Teardown does, would probably be the easiest and most effective way, unless you want to invent some new game-physics math!