Remove calls to deprecated MessageLoop methods on Windows and Linux.

remoting/host/remoting_me2me_host.cc

Index: remoting/host/remoting_me2me_host.cc
diff --git a/remoting/host/remoting_me2me_host.cc b/remoting/host/remoting_me2me_host.cc
index d214fd13dca71c2b7663ce44c4adfcdb8ec4edfb..47fc5d42132f9e5f50bb3c4288148cd9ff1253e1 100644
--- a/remoting/host/remoting_me2me_host.cc
+++ b/remoting/host/remoting_me2me_host.cc
@@ -20,6 +20,7 @@
 #include "base/macros.h"
 #include "base/memory/ptr_util.h"
 #include "base/message_loop/message_loop.h"
+#include "base/run_loop.h"
 #include "base/single_thread_task_runner.h"
 #include "base/strings/string_number_conversions.h"
 #include "base/strings/string_util.h"
@@ -1667,7 +1668,7 @@ int HostProcessMain() {
   new HostProcess(std::move(context), &exit_code, &shutdown_watchdog);
 
   // Run the main (also UI) message loop until the host no longer needs it.
-  message_loop.Run();
+  base::RunLoop().Run();
 
   return exit_code;
 }