Make --install-chrome-app use extensions::WebstoreInstallWithPrompt.

chrome/chrome_browser_extensions.gypi

 # Copyright (c) 2013 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.
 
 {
   'variables': {
     # These variables are shared with the GN build.
     # Name is that these are the extensions files for the extensions target.
     # "chrome_browser_extensions_sources' are the extensions files in the
     # browser target.
@@ skipping 318 matching lines @@
       'browser/apps/app_url_redirector.cc',
       'browser/apps/app_url_redirector.h',
       'browser/apps/chrome_apps_client.cc',
       'browser/apps/chrome_apps_client.h',
       'browser/apps/ephemeral_app_launcher.cc',
       'browser/apps/ephemeral_app_launcher.h',
       'browser/apps/ephemeral_app_service_factory.cc',
       'browser/apps/ephemeral_app_service_factory.h',
       'browser/apps/ephemeral_app_throttle.cc',
       'browser/apps/ephemeral_app_throttle.h',
-      'browser/apps/install_chrome_app.cc',
-      'browser/apps/install_chrome_app.h',
       'browser/apps/per_app_settings_service.cc',
       'browser/apps/per_app_settings_service.h',
       'browser/apps/per_app_settings_service_factory.cc',
       'browser/apps/per_app_settings_service_factory.h',
       'browser/apps/shortcut_manager.cc',
       'browser/apps/shortcut_manager.h',
       'browser/apps/shortcut_manager_factory.cc',
       'browser/apps/shortcut_manager_factory.h',
       'browser/extensions/active_script_controller.cc',
       'browser/extensions/active_script_controller.h',
@@ skipping 851 matching lines @@
       'type': 'static_library',
       'sources': [ 'browser/extensions/api/cast_channel/cast_channel.proto' ],
       'variables': {
           'proto_in_dir': 'browser/extensions/api/cast_channel',
           'proto_out_dir': 'chrome/browser/extensions/api/cast_channel',
       },
       'includes': [ '../build/protoc.gypi' ]
     },
   ],
 }