Install via: https://gist.github.com/Erquint/69ee1acdc34fb9ec6c6f101bbfdcd0e2/raw/Watch2GetherHotkeys.user.js Installing with the `Raw` button can disable updates.

Watch2GetherHotkeys.user.js

// ==UserScript==
// @name        Watch 2 Gether hotkeys.
// @description Space or K plays/pauses, F enables fullscreen. ESC disabled fullscreen as per browsers convention.
// @version     1.0
// @namespace   gness.na@gmail.com
// @author      https://gist.github.com/Erquint
// @homepageURL https://gist.github.com/Erquint/69ee1acdc34fb9ec6c6f101bbfdcd0e2
// @updateURL   https://gist.github.com/Erquint/69ee1acdc34fb9ec6c6f101bbfdcd0e2/raw/Watch2GetherHotkeys.user.js
// @downloadURL https://gist.github.com/Erquint/69ee1acdc34fb9ec6c6f101bbfdcd0e2/raw/Watch2GetherHotkeys.user.js
// @match       http*://*watch2gether.com*/*
// @run-at      document-end
// @noframes
// @inject-into page
// @noframes
// @grant       none
// ==/UserScript==
document.onkeyup = (x => {
    if (x == KeyboardEvent.DOM_VK_SPACE || x == KeyboardEvent.DOM_VK_K) {
      document.getElementsByClassName('w2g-play-button')[0].click();
    } else if (x == KeyboardEvent.DOM_VK_F) {
      document.getElementsByClassName('w2g-dropdown')[1].getElementsByClassName('dd-item')[0].click();
    };
	}
);