What is Illustrator's vector rasterization process?
As as far as I can tell Illustrator has 2 or 3 different rasterizer. The onscreen preview is also prone to the same gap artifacting as your show though its tuned to minimize the effect. Your post seems to imply that your interested in the "art optimized" output.



Image 1: The different render modes of illustrator. Art optimized on left and hinted on right. Note that hinted shows slight background through. I dont have the new CC version so i can not show the third.

How does art optimized work then

Art optimized render mode is simply a un-antialiased image rendered at higher resolution, that has then been subjected to a box filtering. This is called super sampling which is costly. A box filter is simply the mean value of the samples in the box (pixel). This is indeed a similar technology as what the multi pixel filter used in your blender render uses. You can do the same thing manually and get same results. 

In fact the render you get form illustrator is not really good. Its rendered in nonlinear space and not corrected for and you can get better results by swapping to higher order filters and computing in linear color space. All multi sample methods exhibit the same correct rendering (given enough samples even mathematically correct).



Image 2: Multi pixel filtering, on left illustrator native 'Art Optimized'. On right same image at 16x16 pixels with multi lobed Lanczos filter in linear space. Make sure your zoom is 1:1.

The problem

You have in fact come at terms with the real problem of current generation of onscreen renderers. They try to avoid multi sampling in favor for coverage calculation. But it simply can not work perfectly! Simply because alpha blend is:

$$c_0= c_1*\alpha + c_2*(1-\alpha)$$

When chained never reaches 0 when chained over semitransparent surfaces so background show trough. Also it does not know how the coverage is distributed so it will do it wrong. There's simply no way around this in a non-overlapping case like this. but if you allow the shapes overlap then the coverage calculation can be solved (See here).

Other questions You can get same result in any other engine by just simply multisampling a non-antialiased image. You can not get the effect in on screen renderings without doing the overlap trick because they optimize for speed. Does illustrator use 3D? New CC might depends on your interpretation of what 3D is. This issue has nothing to do with 3D just about signal reconstruction methods so its not applicable to the question really.


Related post how-do-i-accurately-compute-coverage-of-overlapping-analytical-curves