Scoring Ping Pong in Elixir
There's a few things you could do to improve this code:

Don't assign inside a case statement.

You assign a value to leader inside this case statement:

scoreDifference =
  case nextPlayer1 &gt; nextPlayer2 do
    true
      -&gt;
      leader = nextPlayer1
      nextPlayer1 - nextPlayer2
    false
      -&gt;
      leader = nextPlayer2
      nextPlayer2 - nextPlayer1
  end


Support for this is deprecated in Elixir, and I assume will eventually be removed.  The Elixir compiler will complain about this when it sees it, and you should listen to it.  Generally you should find a different way to express this.  One option is to return a tuple from your case:

{scoreDifference, leader} =
  case nextPlayer1 &gt; nextPlayer2 do
    true -&gt; 
      {nextPlayer1 - nextPlayer2, nextPlayer1}
    false -&gt; 
      {nextPlayer2 - nextPlayer1, nextPlayer2}
  end


Use if when appropriate.

A cond statement that has one branch with conditions and one true branch is basically just an if statement.  So it'd be simpler to just use an if:

if (scoreDifference + 1) &gt;= 2 and leader &gt;= game.winningScore do
  IO.puts "SOMEONE IS ABOUT TO WIN"
else
  IO.puts "NO-ONE IS ABOUT TO WIN"
end
{:reply, :ok, game}


(I've also moved the reply out of the if statement there, since it was the same across each.  If you wanted to do different things you could move it back in easy enough).

Use Pattern Matching to destructure the scores.

Assuming you are only ever expecting 2 entries in your score list, you could use pattern matching to extract the two scores.  

[nextPlayer1, nextPlayer2] = game.score


I'm not adding 1 to the scores here, because this isn't neccesary to calculate the difference correctly. (It is neccesary to add one to check if someone has a winning score, but I'll come to that).

Simplifying the logic

You can just subtract one score from the other and then call abs on the result to get a positive number for the score difference:

scoreDifference = abs(nextPlayer1 - nextPlayer2)


Then you can find the leader with Enum.max:

leader = Enum.max(game.score)


Putting it all together

If you take all these improvements you might end up with something like:

[nextPlayer1, nextPlayer2] = game.score
scoreDifference = abs(nextPlayer1 - nextPlayer2)
leaderScore = Enum.max(game.score)
if scoreDifference + 1 &gt;= 2 and (leaderScore + 1) &gt;= game.winningScore do
  IO.puts "SOMEONE IS ABOUT TO WIN"
else
  IO.puts "NO-ONE IS ABOUT TO WIN"
end
{:reply, :ok, game}