Remove remaining calls to deprecated MessageLoop methods on Mac.

ppapi/proxy/ppb_message_loop_proxy.h

Index: ppapi/proxy/ppb_message_loop_proxy.h
diff --git a/ppapi/proxy/ppb_message_loop_proxy.h b/ppapi/proxy/ppb_message_loop_proxy.h
index 1613959415148a80f93a828b7cf490b3b952c814..f78c377225409b66dc7566fd7d489a14359c2c93 100644
--- a/ppapi/proxy/ppb_message_loop_proxy.h
+++ b/ppapi/proxy/ppb_message_loop_proxy.h
@@ -13,6 +13,7 @@
 #include "base/macros.h"
 #include "base/memory/ref_counted.h"
 #include "base/message_loop/message_loop.h"
+#include "base/run_loop.h"
 #include "base/single_thread_task_runner.h"
 #include "ppapi/proxy/interface_proxy.h"
 #include "ppapi/proxy/ppapi_proxy_export.h"
@@ -78,6 +79,9 @@ class PPAPI_PROXY_EXPORT MessageLoopResource : public MessageLoopShared {
   base::SingleThreadTaskRunner* GetTaskRunner() override;
   bool CurrentlyHandlingBlockingMessage() override;
 
+  // Quits |run_loop_|. Must be called from the thread that runs the RunLoop.
+  void QuitRunLoopWhenIdle();
+
   // TLS destructor function.
   static void ReleaseMessageLoop(void* value);
 
@@ -88,6 +92,9 @@ class PPAPI_PROXY_EXPORT MessageLoopResource : public MessageLoopShared {
   std::unique_ptr<base::MessageLoop> loop_;
   scoped_refptr<base::SingleThreadTaskRunner> task_runner_;
 
+  // RunLoop currently on the stack.
+  base::RunLoop* run_loop_ = nullptr;
+
   // Number of invocations of Run currently on the stack.
   int nested_invocations_;