What actually happens in Runescape is that certain animations override the running animation. When the animation then ends, the game compensates by making your character move much faster than usual, which can look like zipping all over the place. This is all client side of course; server side your character moves as normal.

Extreme example of someone using this in PVP: https://www.youtube.com/watch?v=kIFWSMW6Lzo