Apparently there is some way to store play (i.e. inputs, timing etc) of a Doom level (Ultimate Doom and Doom II) as text file, so that the precise replay can be replayed on anther person's computer without needing the screen capture. This is said to be particularly useful for speedrunners.
It also gives auxiliary advantages over screen capture since it can be easily read by computer programs which may attempt to catch cheating, or do other interesting things, like game analysis.
Chess also uses this capability, since a whole game can be stored as a Portable Game Notation file.
Is there a general terminology that describes this reproducibility of play in a game?