How to have OutboundPathProcessorInterface change the URL of the loading page
You need three components for this task:

Your outbound path processor UrlRemapOutboundPathProcessor::processOutbound is the first step to get this started.

Second add an inbound path processor UrlRemapOutboundPathProcessor::processInbound to the class similar to Drupal\system\PathProcessor\PathProcessorFiles\processInbound:

  public function processInbound($path, Request $request) {
    if (strpos($path, '/system/files/') === 0 &amp;&amp; !$request-&gt;query-&gt;has('file')) {
      $file_path = preg_replace('|^\/system\/files\/|', '', $path);
      $request-&gt;query-&gt;set('file', $file_path);
      return '/system/files';
    }
    return $path;


Your path processor won't change the URL in the browser, this is by the way the same with other path processors, for example you can access nodes still by their internal paths (/node/[id]) after you've entered an alias.

So third you need a request event subscriber which redirects the unwanted internal URLs. 

An example would be how Redirect does this in RouteNormalizerRequestSubscriber::onKernelRequestRedirect:

 /**
   * Performs a redirect if the URL changes in routing.
   *
   * The redirect happens if a URL constructed from the current route is
   * different from the requested one. Examples:
   * - Language negotiation system detected a language to use, and that language
   *   has a path prefix: perform a redirect to the language prefixed URL.
   * - A route that's set as the front page is requested: redirect to the front
   *   page.
   * - Requested path has an alias: redirect to alias.
   *
   * @param \Symfony\Component\HttpKernel\Event\GetResponseEvent $event
   *   The Event to process.
   */
  public function onKernelRequestRedirect(GetResponseEvent $event) {


http://cgit.drupalcode.org/redirect/tree/src/EventSubscriber/RouteNormalizerRequestSubscriber.php

Probably this global redirect catches the internal paths from step one/two as well. If you don't want to redirect all URLs globally or find issues with the alpha version of this module, you can use this event subscriber as example to write  custom code to target only the specific URLs.