LCD pixels: how chess-board pixel fill patterns are called?
This is due to the panel control driver, and you probably won't find much info about it because this is the secret sauce of each manufacturer.

This is definitely the TV doing that and not the playstation.

The reason behind it is probably, that the driver for each pixel is able to light only at certain amount of brightness, if it is for example a 4 bit per pixel ratio, you will have 16 level of brightness by pixel, for each color.

Now 16 levels per pixel is not a lot, it would give 4'096 different possible colors in total.

But now, if you set different levels per pixel rows, you can drastically increase the amount of possible colors, as anyway from your eye you won't be able to spot single pixels and will only see the average of it.

With only controlling this effect on two rows, you go from 4 bits to 2x 4 bits, this will give you 16'777'216 different possible color, while using the exact same amount of data as before.

So you go from 4'096 color levels to 16+ millions, while driving the panel with the same amount of data. 

It is also probably cheaper to drive individual pixels in 4 bits than 8 bits.

Since 4k panel have a large amount of pixel, this technique is likely used to reduce the bandwidth needed to drive the panel as well as the driver cost, as you need 2x less data for the same result. 

Take the 4 bits per pixel as an example, I do not know how many bit per pixel is being used, but 4 is a likely possibility.



EDIT

Since the TV is given at 1 billion + color, it is possible individual pixels to be driven in 5 bits, with two rows that would give approximately 1 billion colors.

Or that each pixel is driven in 4 bits and that effect is applied on 3 rows, which is more likely as it usually a power of 2.



EDIT 2:

Followed on the comments, it seems to be called "color dithering".