Doom did have networking, using IPX. You had to start the game with a parameter from the DOS commandline. Like Quake, the maps had special player spawn points & items for deathmatch too. The term "deathmatch" was coined by the Doom game mode.
However, there was no frame interpolation in the original Doom, instead, there might be a latency in the inputs. The game state only advances when all players have sent an update for that "tic" (1/35 of a second), so the game might be laggy for everyone if the connection from one of the players is slow.
But multiplayer back then was mostly for LAN parties. At least in my area. I didn't even have an internet connection at that time, personally. In fact, even during the Quake age, I was only able to play on LAN... and I still liked coop better.
Even co-op games have lots of cheating but the nature of the game means the cheating affects people who don’t want to cheat less. They aren’t directly subjected to it, it’s still a problem though, the cheating still affects things like the game economy and player perception of the game.
Yes, what I meant is that cheating becomes irrelevant in coop, not that it doesn't exist.
If a game has an economy that makes some players richer than others (like say.. in many MMOs), and you actually care a lot about being rich in that universe, then it'd starts being more of a competitive thing and less about coop... a game can be competitive and be PvE.
Even singleplayer games can be competitive if you make it about beating your friend's "score" or speed.. almost anything is susceptible to speedrunning.
I guess the question on coop vs competitive is more about what are the goals of the players. If people play games to have a fun time, or if it's because they want to have some way to prove themselves they are good at something :P