Revert of [DevTools] Move DispatchOnDevToolsFrontend to embedder.

content/shell/browser/shell_devtools_frontend.cc

Index: content/shell/browser/shell_devtools_frontend.cc
diff --git a/content/shell/browser/shell_devtools_frontend.cc b/content/shell/browser/shell_devtools_frontend.cc
index 2f417ac3a36d8ab4b8032232f5d563aba12ea563..fe30eddef0c8e94ebb52eb416e94017c8683a661 100644
--- a/content/shell/browser/shell_devtools_frontend.cc
+++ b/content/shell/browser/shell_devtools_frontend.cc
@@ -143,9 +143,8 @@
 
 void ShellDevToolsFrontend::DispatchOnInspectorFrontend(
     const std::string& message) {
-  std::string code = "InspectorFrontendAPI.dispatchMessage(" + message + ");";
-  base::string16 javascript = base::UTF8ToUTF16(code);
-  web_contents()->GetMainFrame()->ExecuteJavaScript(javascript);
+  if (frontend_host_)
+    frontend_host_->DispatchOnDevToolsFrontend(message);
 }
 
 void ShellDevToolsFrontend::InspectedContentsClosing() {