(See the best response by Lummox JR.)
                    for (int i = 0; i < 11; i++) { // for loop
var/temp = board[i];
var/nick = Names[i];
if (board[i] > Points) {
board[i] = temp;
Names[i] = nick;
else if (board[i] != Points) {// If Begins here
board[i] = Points;
Names[i] = Pname;
}//end of if statement

Problem description:
For reference, I placed the initial values for the 'board' list as -666 to ensure that my if loop goes through.And it does -- the only problem is that everytime I get a new score, it overwrites EVERYTHING with said score.
Honestly, you have said what the problem is, but I am not sure you provided enough information (hence the lack of responses). Your snippet is cryptic to someone who knows nothing about how your system is supposed to work; I think you should post everything having to do with scoring and better explain how the system is supposed to work vs. what it is actually doing.
Best response
When you said slot machine, I thought you meant you were using some sort of slot machine mechanic in your game. As I understand it this is a slot in a high score table, instead.

Here's where you're going wrong: At each stage in the loop, you're replacing the current person with the new one, if the new score is higher than theirs. So naturally, this will replace everyone below that score.

However, this code isn't DM; it doesn't appear to be any specific language. The var statements are DM syntax, but the for() loop is using semicolons instead of commas, is declaring a var as "int", and is using a 0-based list index. Are you writing something in JavaScript for the webclient, or what? I can offer code suggestions, but I need to know which language you're working with.