How does one define a "Pure" FPS experience?
Is a Pure FPS a solo-play adventure, pitting the player against the gaming environment?
Is a Pure FPS about Humans vs Humans, competing in a true test of skill?
Is a Pure FPS about working together, or standing alone?
Is it about starting on equal footing, or unbalanced play where skill, tactics, planning or just being lucky enough to spawn next to the rocket launcher decides the winner?
Should a Pure FPS make you laugh along with the absurdity of it all, or make you shit yourself with terror?
If we are going to consider the FPS as a solo-play execution of absolute mayhem, then DOOM has to take it. DOOM is a non-stop frag-fest from the word go, with the 'puzzles' of the game being little more than "Go to A, B, C then the Exit, fighting off sixty+ ambushes along the way". Despite the ancient graphics, primitive sound and laughable physics engine, DOOM is still capable of inducing more terror in a player than the Chimera Combine and Covenant combined.
However, if we are going to consider the "Pure" FPS as a test of skill, where luck is minimalised as much as possible, then I'm inclined to go with the Resistance series. The multiplayer is very balanced, and in Deathmatch at least victory should go to the most skillful player... as opposed to the likes of Halo 3, where victory goes to whoever picks up the Spartan Laser first.
Finally, if we wish to consider the FPS' pedigree by story, then Half Life 2 (and its progeny) has to be the winner. I have never experienced a story so gripping, and so wondrously executed in any other FPS. Hell, even some RPGs fail in comparison!