I'm a huge fan of the Doom games. I have played or own every single console release of the game, and know the ins and outs of each version with quite frightening detail - from the music-less Atari Jaguar version and the texture-less floors and ceilings of the SNES port, to the windowed 3DO and 32X versions and the sublime multi-coloured PS1 iteration. I've also played the PC originals to death and more recently the Brutal Doom mod on my mac...yet my personal favourite has got to be Doom 64. You can read about my love for that game here if you so wish, but let's get down to business - you've come to the Dreamcast Junkyard for DC-related prose, not N64 circle-jerking.
Sadly, the Dreamcast never got an official retail port of id Software's genre-defining shooter, which is understandable when you consider the timing of the console's release and lifespan. It was probably too late to put the original games out as an official release, and too early for Doom 3; plus the idea of semi-retro compendiums was quite new at the time and so a re-issue would probably have been derided as unnecessary, and a bit of an insult to those people who had shelled out for a 128-bit system. While retro collections are all the rage these days, back in the early 2000s they simply were not the de rigueur. That said, Doom 3 was years away from release and the game we all know today would have been far too much for the Dreamcast to handle with it's complex vertex shading and texturing techniques - even the original Xbox had to make do with a heavily compromised port of the PC game.