If there's interest in playing with such technologies then I suggest reading up on z-fighting because if you understand why it happens then you can attempt to work around it. There are lots of old tips and tricks that still apply today.
Thinking it over I may be incorrect in referring to this in the way I have. The issue I'm seeing is the back-to-front rendering (I'm assuming this is what the example is doing) of a smaller object being displayed on top of larger object and the renderer getting confused on the draw order.
Edit: ghusbands points out my confusion below
Granted, I'm not a 3D programmer but I built enough levels for 3D engines back in the day to have to be aware of these issues to design around them. This is all from memory so I could be totally off but this what it seems to me.