Settings Router Refactor: Migrate to settings.Route.navigateTo calls.

chrome/browser/resources/settings/device_page/device_page.js

 // Copyright 2016 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 /**
  * @fileoverview 'settings-device-page' is the settings page for device and
  * peripheral settings.
  */
 Polymer({
   is: 'settings-device-page',
@@ skipping 10 matching lines @@
       type: Object,
       notify: true,
     },
   },
 
   /**
    * Handler for tapping the Touchpad settings menu item.
    * @private
    */
   onTouchpadTap_: function() {
-    this.$.pages.setSubpageChain(['touchpad']);
+    settings.navigateTo(settings.Route.TOUCHPAD);
   },
 
   /**
    * Handler for tapping the Keyboard settings menu item.
    * @private
    */
   onKeyboardTap_: function() {
-    this.$.pages.setSubpageChain(['keyboard']);
+    settings.navigateTo(settings.Route.KEYBOARD);
   },
 
   /**
    * Handler for tapping the Display settings menu item.
    * @private
    */
   onDisplayTap_: function() {
-    this.$.pages.setSubpageChain(['display']);
+    settings.navigateTo(settings.Route.DISPLAY);
   },
 });