The Score Display option shows up in the additional rules after being unlocked.
The Score Display appears once it has been turned on.
Score Display is an unlockable feature introduced in Super Smash Bros. Melee. It can be unlocked by scoring a combined total of 5,000 KO's in VS Mode. Once unlocked (and turned on), you will now see your KO score on-screen (amount of KO's by numbers), instead of waiting until the end of a match to view it. The option, however, doesn't work in certain matches such as Stock.