I found this to be a pretty good layman's explanation, hopefully this helps you understand. The problem with the tests you linked above is that it was using spare SSDs doing nothing but writing benchmarks. Try running those benchmarks when you're also running the OS on the same drive or playing a game and the results would be vastly different. Below is a snippet of an article written by Aaron Mickunas at Riot Games.
When you save a file to your computer, your SSD has to do some (very) quick math to determine where on the drive the data should be saved. It figures out where the next empty space on the drive is, and it fills it with the new data. Simple enough, but it can get a little hairy.
When data on a block is changed, the SSD needs to recalculate over and over again. Meaning, although the data already exists in a block somewhere on the drive, in order to change the data, it needs to find another blank block and move it there. Why? Because it cannot write data to a block unless that block is empty. If the SSD tried to change data that already exists in a block, it would destroy the data.
Write amplification: a sliding block puzzle for your SSD.
Music Sorter at English Wikipedia,
CC BY-SA 3.0
Writing new data entails copying the data from the existing block to a new, empty block, but with the changes included. The drive then marks the previous block as ready to be overwritten, so it can be used as an empty space for the next file that needs it.
For a single file, this process doesn’t really mean anything. But in a game, when things change on-screen very often, or in bulk when you load a saved game, it needs to happen on a much larger scale all at once. We’re talking hundreds or thousands of data rewrites. If the process is slowed down by even a fraction of a fraction, it adds up, even if the SSD can do all of this in a matter of seconds.