What is it? Cheat? How this players move so fast? No, it called hook. Some servers in Quake 3 support this great feature. For use it you need bind free button in your keyboard or mouse. You must open game console. This is button ~ under ESC. And type there:
\bind f +button5 - it mean button f will use for hook. You can bind any free buttons not only f.
Or for mouse:
\bind mouse2 +button5 - it mean you will use for hook right button of mouse.