I have to completly agree with ssj12 on Unreal, and rocketpig on other things...
But Unreal didn't start online FPS gaming, Online FPS Gaming started with Quake & Duke3D. After that, online gaming exploded with games like Unreal Tournament, Counterstrike, Tribes, Quake 2
It was the combination of online networks like Mplayer & Total Entertainment Network that started online gaming (GameSpy came afterwards)