id changed Doom's license to GPL in 1999. Scroll down to October 3 on this page: https://web.archive.org/web/20000818041410/http://www.doomwo.... I believe the confusion comes from when id uploaded the Doom source to Github, they uploaded an older version with the original license headers rather than the newer GPL version.
At the time it was claimed that it was dual licenced both with the original licence and GPLv2. So presumably if and only if you were wanting to sell modified versions the source code to them must be made available. It seems the GPLv2 licence came about as around 1999 some source ports were releasing binaries only. https://www.youtube.com/watch?v=_jsahAmb8s4