From watching the replay, the "teleporting" portion of the hack appears to be that they can grant themselves a very large amount of horizontal momentum instantaneously, probably on a button press. Something along the lines of a 5x or 10x dash, but without consuming any stamina, and with no cooldown.
The aimbot is an aimbot, seems to just center screen on nearest hero if there is a hero nearby, or nearest creep if not.
And they also seem to have a quickscope macro but that could just be a standard mouse macro