Remove all remaining traces of MessageLoopProxy.

chrome/browser/engagement/site_engagement_service.cc

 // Copyright 2015 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "chrome/browser/engagement/site_engagement_service.h"
 
 #include <stddef.h>
 
 #include <algorithm>
 #include <utility>
@@ skipping 91 matching lines @@
   }
   const std::string group_name =
       base::FieldTrialList::FindFullName(kEngagementParams);
   return !base::StartsWith(group_name, "Disabled",
                            base::CompareCase::SENSITIVE);
 }
 
 SiteEngagementService::SiteEngagementService(Profile* profile)
     : SiteEngagementService(profile, base::WrapUnique(new base::DefaultClock)) {
   content::BrowserThread::PostAfterStartupTask(
-      FROM_HERE, content::BrowserThread::GetMessageLoopProxyForThread(
+      FROM_HERE, content::BrowserThread::GetTaskRunnerForThread(
                      content::BrowserThread::UI),
       base::Bind(&SiteEngagementService::AfterStartupTask,
                  weak_factory_.GetWeakPtr()));
 
   if (!g_updated_from_variations) {
     SiteEngagementScore::UpdateFromVariations(kEngagementParams);
     g_updated_from_variations = true;
   }
 }
 
@@ skipping 456 matching lines @@
     if (!engagement_score.last_shortcut_launch_time().is_null() &&
         engagement_score.last_shortcut_launch_time() > last_visit) {
       engagement_score.set_last_shortcut_launch_time(last_visit);
     }
 
     engagement_score.Commit();
   }
 
   SetLastEngagementTime(now);
 }