Right, my objection to the textured cubes is that they are not the volume equivalent of a pixel. Pixels are point samples without shape or texture. These cubes have both.
What I call a voxel is much smaller (on the order of a screen pixel), and drawn as a point sprite or screen-facing quad with a single color. Texturing is achieved by having many voxels with different colors/materials.
Here are some videos of what we used to call voxels:
Note that they were not using voxels because they had a certain artistic style to them. They used voxels because with the hardware they had, this was the most realistic rendering they could achieve. Once GPUs came out with hardware-accelerated triangle rasterization, voxel engines died.
For more information about point-sampling, see this classic paper, "A Pixel Is Not A Little Square":
I'm a bit confused about what distinction you're trying to make, or how this project represents a change in the meaning of the word 'voxel'.
Voxels are "volumetric cells" just like pixels are "picture cells". The size of them has absolutely nothing to do with it, and never has. Big voxels are still voxels. The data in the file is specified as volumetric samples... Maybe the issue is the texture you're talking about, but I haven't seen any textures in any of the galleries, other than the few examples that render mesh edges in addition to the cubes. Where are you seeing textures?
Six square polygons enclosing a space is surely just as 'voxel' as meshes generated by marching cubes for medical imaging. I've worked in medial imaging, written more than one volume renderer and used used many more than that, for both games and research. As far as I'm concerned, Magica Voxel is both truly voxel and truly awesome, IMO.
Alvy Ray Smith's paper is great, but how to handle sampling is a different subject completely from whether the scenes are volumetric, which they are. These voxels do have a certain artistic style to them, and the aesthetic choice to give them sharp edges was made intentionally and called out explicitly, i.e., "8-bit".
Voxels with a texture index vs. voxels with a color index is not really a big distinction in my eyes. They're both integers. The way in which you resample them, as well, is not invalidating. Otherwise "pixel art" would also be invalid as it's built around display output methods that are not mathematically correct(NTSC signal, square LCD pixels, etc.).
What I call a voxel is much smaller (on the order of a screen pixel), and drawn as a point sprite or screen-facing quad with a single color. Texturing is achieved by having many voxels with different colors/materials.
Here are some videos of what we used to call voxels:
DOS game: https://www.youtube.com/watch?v=51E_G7NCXVM
Gameboy game: https://www.youtube.com/watch?v=3zVy-4CEFQU
Medical imaging: https://www.youtube.com/watch?v=GrLqFNhVL68
Note that they were not using voxels because they had a certain artistic style to them. They used voxels because with the hardware they had, this was the most realistic rendering they could achieve. Once GPUs came out with hardware-accelerated triangle rasterization, voxel engines died.
For more information about point-sampling, see this classic paper, "A Pixel Is Not A Little Square":
http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf
And for a more in-depth discussion of sampling, albeit in one dimension, watch Chris Montgomery's video "Digital Show and Tell":
http://xiph.org/video/vid2.shtml