This video is not based on a specific letter, but on multiple fan letters. Eminem even said in an interview that he gets letters as much or more crazy than those of "Stan".
The word "Stan" has become so popular in modern culture that it even entered the Oxford Dictionary in 2018, as a noun (stan) as well as a verb (stans, stanning, stanned). It is described as "An overzealous or obsessive fan of a particular celebrity".
The chorus in this song is sampled from the Dido song "Thank You".
At the end of the video when Eminem realizes that Stan is dead, the window next to him shows lightning flash and you can see Stan staring at him for a brief moment.
There is a long version and a short version of this video. The short version is around 6 min., while the long version is around 8 min. To make the short version shorter, the second verse was cut down.