If 2K referred to the number of pixels, it would look like this:
FullHD is actually a little over 2M pixels.
takes the aspect ratio from 3:4 to 16:9. so pixel density is barely better
What? Screen aspect ratio and pixel density are quite different things. Most FullHD TVs are widescreen and have pixel density below 36 ppi, and while high-DPI 4:3 screens are rare, they are not impossible in any way.
1080 rows of 1920 pixels each
1920 columns of 1080 pixels each