Don't pointerify [☺] User Name nor user@name.com In the top, right corner of chrome://apps.

chrome/browser/resources/ntp4/new_tab.css

 /* Copyright (c) 2012 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. */
 
 html {
   /* It's necessary to put this here instead of in body in order to get the
      background-size of 100% to work properly */
   height: 100%;
   overflow: hidden;
 }
@@ skipping 215 matching lines @@
   -webkit-transition: none !important;
 }
 
 /* Login Status. **************************************************************/
 
 #login-container {
   background: transparent none;
   border: none;
   box-shadow: none;
   color: inherit;
-  cursor: pointer;
   font: inherit;
   /* Leave room for the scrollbar. */
   margin-left: 13px;
   margin-right: 13px;
   margin-top: 5px;
   padding: 0;
   position: fixed;
   right: 0;
   text-align: right;
   top: 0;
   z-index: 10;
 }
 
+#login-container:not(.signed-in) {
+  cursor: pointer;
+}
+
 html[dir='rtl'] #login-container {
   left: 0;
   right: auto;
 }
 
 #login-container [is='action-link'] {
   -webkit-margin-start: 0;
 }
 
 .login-status-icon {
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   padding: 0;
 }
 
 .other-sessions-promo-message:only-child {
   display: block;
 }
 
 .other-sessions-promo-message p {
   margin: 0;
 }