This is why existing voxel games tend to look super blocky and pixelated.
That said - they seem to have solved that for non-organic forms at least (their video forms are very cool, but are basically frame by frame volumetic animation - a little different).
Lighting will be the big issue, though not always a problem in all games.
I'm assuming by this you mean each frame using a distinct voxel model.
I may be wrong, but I think what's being demoed at 0:47 in the video is animation by deformation of a static model. If true, this is something I've not seen in voxel graphics before.
Unfortunately, the article is very light on the details about what is technologically novel about what Atomontage is doing, versus previous endeavours.
That said if they can do just non-organic forms well and leave organics to polygons - that would be pretty incredible.