JSFiddle - React, Tailwind, and code Playground

HTML

<div class="sixteen columns"> 
    <div id="applicationStatus">
        <ul class="applicationStatus">
            <li class="applicationStatus">Application Received</li>
            <li class="applicationStatusGood">Language Exam</li>
            <li class="applicationStatusNoGood">Oral Exam</li>
            <li class="applicationStatus">Grant</li>
        </ul>
    </div>
</div>

CSS

#applicationStatus {
  position: relative;
  width: auto;
  height: 140px;
  left: 40px; }

.applicationStatus li { /* Added this and moved much code to here */
  position: relative; /* this was a key property missing from your code */
  text-indent: 30px;
  height: 140px;
  background-color: #767676;
  display: inline-block;
  /* Dirty IE Hack */
  zoom: 1;
  *display: inline;
  /* margin-right: 30px; Eliminated this */
  margin-left: 30px;
  padding: 10px 10px 10px 30px;
  color: white;
  font-size: 18px;
  text-align: center;
  line-height: 150px;
}

ul.applicationStatus { /* this is irrelevant with the HTML you gave, but I added the class */
  list-style: none; }

li.applicationStatus:first-child:after, li.applicationStatusGood:after, li.applicationStatusNoGood:after {
    content: "";
    position: absolute;
    width: 0;
    height: 0;
    border-top: 80px solid transparent;
    border-left: 30px solid #767676;
    border-bottom: 80px solid transparent;
    margin: -10px 90px 0 10px; 
}
li.applicationStatus:last-child:before, li.applicationStatusGood:before, li.applicationStatusNoGood:before {
    content: "";
    position: absolute;
    width: 0;
    height: 0;
    left: 0;
    border-top: 80px solid transparent;
    border-left: 30px solid white;
    border-bottom: 80px solid transparent;
    margin: -10px 0px 0 0px; 
}

li.applicationStatus:first-child {
    padding-left: 10px;
    margin-left: 0;
}
li.applicationStatus:last-child {
    padding-right: 30px;
}

li.applicationStatusGood {
  background-color: #77a942; }
  li.applicationStatusGood:after {
    border-left: 30px solid #77a942; }

li.applicationStatusNoGood {
  background-color: #c42c00; }
  li.applicationStatusNoGood:after {
    border-left: 30px solid #c42c00; }