Remove calls to deprecated MessageLoop methods on Windows and Linux.

services/navigation/content_client/browser_main_parts.cc

Index: services/navigation/content_client/browser_main_parts.cc
diff --git a/services/navigation/content_client/browser_main_parts.cc b/services/navigation/content_client/browser_main_parts.cc
index a704380537cd717ce668e2a56ac388554ffb6431..ec1858391662d3841df15944aad636f90d0b0156 100644
--- a/services/navigation/content_client/browser_main_parts.cc
+++ b/services/navigation/content_client/browser_main_parts.cc
@@ -5,6 +5,7 @@
 #include "services/navigation/content_client/browser_main_parts.h"
 
 #include "base/message_loop/message_loop.h"
+#include "base/run_loop.h"
 #include "content/public/common/mojo_shell_connection.h"
 #include "content/shell/browser/shell_browser_context.h"
 #include "content/shell/browser/shell_net_log.h"
@@ -42,7 +43,7 @@ void BrowserMainParts::PostMainMessageLoopRun() {
 }
 
 bool BrowserMainParts::MainMessageLoopRun(int* result_code) {
-  base::MessageLoop::current()->Run();
+  base::RunLoop().Run();
   return true;
 }