Set kAppType to system level windows as well.

IME uses this propery to tell if it's arc windows.
With this fix, text input on type type window (e.g.
FB ChatHead) works again.

BUG=b/111713229
TEST=manual. See bug for repro step.

Change-Id: Ifa058f3a4c4c91daf7059311044c4440780f47ad
Reviewed-on: https://chromium-review.googlesource.com/1148237Reviewed-by: Yury Khmel <khmel@chromium.org>
Commit-Queue: Mitsuru Oshima <oshima@chromium.org>
Cr-Commit-Position: refs/heads/master@{#577633}

chrome/browser/ui/ash/launcher/arc_app_window_launcher_controller.cc

@@ -210,6 +210,12 @@ void ArcAppWindowLauncherController::AttachControllerToWindowsIfNeeded() {
 void ArcAppWindowLauncherController::AttachControllerToWindowIfNeeded(
     aura::Window* window) {
   const int task_id = GetWindowTaskId(window);
+  if (task_id >= 0) {
+    // System windows are also arc apps.
+    window->SetProperty(aura::client::kAppType,
+                        static_cast<int>(ash::AppType::ARC_APP));
+  }
+
   if (task_id <= 0)
     return;
 
@@ -220,8 +226,6 @@ void ArcAppWindowLauncherController::AttachControllerToWindowIfNeeded(
   // TODO(msw): Set shelf item types earlier to avoid ShelfWindowWatcher races.
   // (maybe use Widget::InitParams::mus_properties in cash too crbug.com/750334)
   window->SetProperty<int>(ash::kShelfItemTypeKey, ash::TYPE_APP);
-  window->SetProperty(aura::client::kAppType,
-                      static_cast<int>(ash::AppType::ARC_APP));
 
   // Create controller if we have task info.
   AppWindowInfo* info = GetAppWindowInfoForTask(task_id);