I don't know about the F1 game but I can take a guess on Gunstar Heroes.
I noticed the cubes are always aligned perfectly to the axis. And they have an isomorphic projection so the cube is always the same height (although that shouldn't be strictly necessary) as it's rotating. I also noticed the cubes never seem to get smaller if they are closer to the background.
Because of this you could just have a series of sprites each showing the cube in a different angle of rotation.
Now all you need to do is properly position a bunch of sprite (16 cubes + head) and it looks like a bunch of cubes that are actually drawn in 3-D. It wouldn't surprise me if they have some small table of the X/Y positions of the cubes precomputed so they don't have to do that in real time.
In fact since every cube is always rotated at the same angle you could just have one sprite in the system table and update it every frame.
That's my guess anyway. Clever sprite trickery.
It wouldn't surprise me if F1 uses something closer to what is described in the article (although much less capable).