Build public cast_shell on x86 with GN.

chromecast/common/BUILD.gn

 # Copyright 2015 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.
 
+import("//chromecast/chromecast.gni")
+
 source_set("common") {
   sources = [
     "cast_content_client.cc",
     "cast_content_client.h",
     "cast_resource_delegate.cc",
     "cast_resource_delegate.h",
     "global_descriptors.h",
     "platform_client_auth.h",
     "pref_names.cc",
     "pref_names.h",
   ]
 
-  # TODO(kmackay) Add "platform_client_auth._simple.cc" to sources
-  #               if chromecast_branding != "Chrome"
+  if (chromecast_branding == "public") {
+    sources += [ "platform_client_auth_simple.cc" ]
+  }
 
   deps = [
     "//base",
     "//chromecast/base:cast_version",
     "//content/public/common",
     "//ui/base",
     "//ui/gfx",
   ]
 }