Rock Paper Scissors in JavaScript
The definition of the winningMap is very confusing. 

I suggest a different form of input: 

var winningMap = {Rock: "Scissors", Paper: "Rock", Scissors: "Paper"}; 


It defines which choice can be beaten by a specific selection. 
If both inputs are the same, it's obvious a tie:

var getWinner = function (playerChoice, computerChoice) {
    if(playerChoice === computerChoice){
        return "Tie";
    }
    if(computerChoice === winningMap[playerChoice]){
        return "Player Wins";
    }
    return "Computer Wins";
};


Notice, that I didn't use the string-definitions. I don't think that it's necessary, and it only makes the code a bit more complicated.

In order to convert the computer's choice to an actual string (Rock, Scissors, Paper), you can use an Array:

var stringMapping = ["Rock", "Scissors", "Paper"];

var getComputerChoice = function () {
    return stringMapping[ Math.floor(Math.random() * 3) ];
};


Maybe a new-Operator would be understood easier

The closure might be confusing for a beginner, maybe you should consider to write the Object this way:

function RockPaperScissors (){ 
     var getComputerChoice = function(){ ... };    //= private variable
     this.getWinner = function(){ ... };           //= public variable
};

var actualObject = new RockPaperScissors();
actualObject.method();
actualObject['method']();


If your colleagues are used to object oriented programming, this style might be more familiar.

Always use brackets

if ($input.val() === '-1') { return; }


I personally don't mind conditions within one line, but dropping the brackets is bad practice - and can lead to strange behaviours, especially in JavaScript.

Furthermore, I wonder why u used the dollar-sign at the beginning of the $input-variable?

Edit:

I share @Barts's opinion from the comments - it's not neccessary to use jQuery in this example. You should show them jQuery once they know the basic principles of JavaScript.