Hmm. An interesting thread.
I think that Doom is one of those games which can genuinely be described as hugely influential, for various reasons:
-First quality mainstream 2.5d FPS (wolf3d had flat levels). Quake deserves credit too for going properly 3d.
-HUGELY popular shareware game (~10 million downloads within 2years, at a time when hardly anyone had the internet)
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Network gaming/deathmatch. This is probably the most important, in the mid90s Doom had people going crazy over this incredible new experience. Over 10 years later and the basic principles of deathmatch have changes little
But, to be fair, it wasn't until Quake that we saw the client<->server model which we know and love.
-Mapping/Modding. People can bleat on about Q2 all they want, but the Doom WAD scene was what spawned we know today. Quake deserves a mention here too of course, as that really took things to the next level.
-Boosting the hardware market. Doom was the killer app, the game which made people sit up and say 'jeez, I thought PCs sucked for games, but this is something else!'. People even went so far as upgrading to 486s or more memory for better performance/visuals. Again, Quake did the same for the pentium and 3d accelerator markets.
As regards the networking/deathmatch thing however, I do wonder what would have happened if another mainstream game from a different genre had come out offering network multiplayer which was so much goddamned fun. Maybe instead of FPS another genre would have taken off. I'm neglecting online RPGs (MUDs etc) at this stage because they weren't really mainstream games you could buy in the shops.