App.svelte

<script>
  import Controller from './game/Controller.svelte';

  function handleGlobal (ev) {
    console.log('handleGlobal on App!');
    console.log(ev);
  }
</script>

<h1>Hello!</h1>
<Controller></Controller>

<svelte:window on:global={handleGlobal}></svelte:window>

Controller.svelte

<script>
  function handleClick() {
    const ce = new CustomEvent('global');
    ce.data = {a : 'b'};
    window.dispatchEvent(ce);
  }
</script>

<button on:click={handleClick}>Global event!</button>