How does one create this effect and be able to control the level of dithering?
For Eevee, the principle is similar to the one used in this answer.
Simply you can change the input parameters and play with the Voronoi texture options.
I've changed few things to the node setting.
Voronoi input is set to camera texture coordinates.
Voronoi changed to 2D and distance to edge.
Inputs on the right tuned.
I have written a detailed breakdown of the shader as a medium post. Here is what the result looks like. The .blend file is attached below.
The main idea is to create a map from grayscale to the dithering patterns. Once you have created this, you can use the Diffuse BSDF node to create the shading, which will be mapped to the corresponding patterns.
I use the camera coordinates to create the pixel index.
The pixel index can be turned into different patterns using simple modulo arithmetic. The checkered pattern would be mod(x+y,2). Here is another example.
Once you have all the patterns, create a map from the grayscale to the patterns.
Add them together and use the pattern as the factor input of the Color Mix node.
Left is the Diffuse BSFD only, and right is after the mapping.