How do I get the reference to an existing YouTube player?

A great way to do this without loading the IFrame API in the parent window is to grab the object from the IFrame

var ytplayer_window = document.getElementById("playerIFrame").contentWindow;
var player = ytplayer_window.yt.player.getPlayerByElement(ytplayer_window.player);

Maximus S gave a perfectly correct answer. The official YouTube IFrame Player API docs suggest initialising the player through a unique id of an iframe with the video as var yPlayer = new YT.Player('unique-id');.

For the future readers of this question looking for a way to generate a YouTube Player from a reference to an iframe element without id (as myself), it is possible to do so by running var yPlayer = new YT.Player(iframeElement); if you add type="text/html" attribute to the iframe element and set enablejsapi=1 parameter in the src attribute:

<iframe type="text/html" height="360" width="640" src="https://www.youtube.com/embed/jNQXAC9IVRw?enablejsapi=1"></iframe>

Full snippet

This can be done like the following.

Given a general YouTube embed source code:

<iframe width="560" height="315" src="//www.youtube.com/embed/M7lc1UVf-VE" frameborder="0" allowfullscreen></iframe>

a. Add a enablejsapi query param and set it to 1 in the src URL

<iframe width="560" height="315" src="//www.youtube.com/embed/M7lc1UVf-VE?enablejsapi=1" frameborder="0" allowfullscreen></iframe>

b. Give it a unique id

<iframe id="youtube-video" width="560" height="315" src="//www.youtube.com/embed/M7lc1UVf-VE?enablejsapi=1" frameborder="0" allowfullscreen></iframe>

c. Load YouTube iFrame API

<script src="https://www.youtube.com/iframe_api"></script>

d. Create a player that references the existing iFrame

var player;
function onYouTubeIframeAPIReady() {
  player = new YT.Player('youtube-video', {
    events: {
      'onReady': onPlayerReady,
      'onStateChange': onPlayerStateChange
    }
  });
}

function onPlayerReady() {
  console.log("hey Im ready");
  //do whatever you want here. Like, player.playVideo();

}

function onPlayerStateChange() {
  console.log("my state changed");
}

var player = YT.get('id-of-youtube-iframe');