Quake III Arena defined Deathmatch.
Unreal Tournament deifned Team Deathmatch.
TFC 1.5/Half-Life redefined Capture the Flag and help push incredible game modes we see today.
You are young, the way I remember it:
DOOM2 defined deathmatch (and PC games at all)./
Q2 LMCTF then Q3 RA3 were the best CTF and Team Deathmatch games ever made. Everything since has just been techno crap.