There is no single reason why the "wildcat" works for Neal Brown and UK. One good reason it works, however, is because of the numbers advantage UK gets at the line of scrimmage, and especially at the point of attack. Every offensive formation must have 7 men on the line of scrimmage. When UK runs its wildcat package it replaces 2 wide receivers for a fullback and a tight end. It then splits Towels out wide as a receiver on the line of scrimmage leaving only the running back and the fullback in the backfield. This give the offense 6 blockers on the line of scrimmage and 1 blocker in the backfield for 7 total blockers. The defense aligned so as to have 8 at the line of scrimmage to defend the run.
UK gains a numbers advantage by not blocking the two men on the end of the defensive line of scrimmage. One they will allow to come free and let Kemp use his speed to beat him to the line, and the other is "blocked" with the jet motion which comes across the formation. That defender is the "force" player and if he ignores the Jet motion, UK will call the jet sweep and let him run free to the outside edge. By failing to block two defenders, UK has 7 players to block 6.
To gain an advantage at the point of attack, UK will pull the guard opposite the tight end to lead onto the linebacker. This gives UK 5 players to block 3 at the direct point of attack.
From there, UK simply executes their blocks better than South Carolina can shed. The tight end and the tackle will double team the defensive end into the lap of the linebacker. The fullback leads between the tackle and the guard to clear out any fill. The Play-side guard handles the defender head up to inside of him with the center blocking backside. The backside guard pulls around and moves out the filling weak side linebacker. The left tackle does a wonderful job cutting off penetration from the gap left by the pulling guard.
From there, Kemp simply plays running back.
Here are a few clips narrated. Enjoy.