I thought it was generally agreed (by whom I'm not sure, let's just say public opinion) that Quake 3 is the purest, most distilled deathmatch FPS to the point where it is the quintessential game to use when explaining what deathmatch is all about. Now I didn't play it much online as dialup was a shocking way to play a multiplayer FPS and even if I could, I probably would have sucked anyway. But it still was incredibly popular and even played without any mods it has a simplicity and charm that I think is rather appealing.
Having said that, Quake 3 appears to have been designed so that it would appeal to the pro gamers which was an emerging concept at the time and hence this "soul" as you call it may have been lost when designing the game. Similar complaints have been made about StarCraft II - that it's not as fun as the original because it was designed to accommodate pro gamers and e-sports, and so some of the soul of the original (which didn't have this aim at all) didn't transfer into the sequel.
Anyways, it's all good nostalgia. I still have all the Quake games and play them occasionally with newer engines as they are extremely quick to load, play and do things with (modern games have too many unskippable movies, animations in the menus to slow things down and waste time connecting to online services with pointless achievements). But maybe I'm a grumpy old man. :)