What your looking at there, if you wanted to make it with Blender would be easiest with material ID pass (which makes each material a separate colour) and then some fancy compositing.
Seriously, most of the effect in that video will come from post processing, so I suggest looking into that. Blender’s compositor if Blender is what you want to look at.
Here’s an example I made, just with Blender:
This is the material for the plane I pointed the camera at, it just generates a random coloured noise (like in your image)
This is the compositing nodes, which takes your input image, using the Greater than or ‘>’ node to posterise your image, and then combines it with the render, which is the coloured image generated from the first step. This is the important part.
This is the result it generates: