He was supposed to race the finish and dodge the cars, but instead he just let himself get flung by the cars and cross the finish line quickly

Basically it is TAS levels of Smash Directional Influence (SDI), where in hitstun you can move yourself a few pixels at a time for a few frames.

With each F-Zero machine C. Falcon gets hit by, he SDI's backwards to get hit by more of the vehicles, individually SDIing each hit, and using the knockback and momentum achieved to perform frame perfect movements to travel all the way to the goal.

TL;DR, TAS Melee is broken