Single player
Single player is the baseline game mode in Doom, inherited from Id Software's previous games such as Wolfenstein 3D, as multiplayer was added as an experiment.
Single player is not defined entirely by the amount of human players, since it is possible to play in cooperative or deathmatch mode while being alone with the addition of computer bots.
Competition is possible in single player through demo recording and speedrunning. The old "Doom Honorific Titles" required a player to demonstrate the ability to complete levels in single player mode while fulfilling specific conditions.
Thing placement
In vanilla Doom and Heretic, things appear in single player mode unless the "multiplayer only" flag is set. Boom added the "not deathmatch" and "not cooperative" thing flags, allowing to have things that only appear in single player mode. Hexen introduced a different system where flags are explicitly set to mark a thing as appearing in single player, deathmatch, and cooperative game modes. ZDoom uses the same approach in UDMF.
Death
When the player dies in this game mode, the last savegame made is reloaded, and in the absence of saves the level is reset and the player has to start it again from a pistol start.