Why doesn't nth-of-type/nth-child work on nested elements?

:nth-of-type() is similar to :nth-child() in that they must all be from the same parent. If you need those wrapper divs, use :nth-of-type() on those wrappers instead:

div.post:nth-of-type(odd) .video-entry-summary {
    width:214px; 
    height:210px; 
    margin-left:0px;
    float:left;
    position:relative; 
    overflow:hidden; 
    border:1px solid black; 
    background:#ccc; 
}

If all the siblings are .post, use :nth-child() instead to prevent confusion with what :nth-of-type() really means:

.post:nth-child(odd) .video-entry-summary {
    width:214px; 
    height:210px; 
    margin-left:0px;
    float:left;
    position:relative; 
    overflow:hidden; 
    border:1px solid black; 
    background:#ccc; 
}

.video-entry-summary {
  width: 214px;
  height: 210px;
  margin-left: 10px;
  float: left;
  position: relative;
  overflow: hidden;
  border: 1px solid black;
}

.post:nth-child(odd) .video-entry-summary {
  width: 214px;
  height: 210px;
  margin-left: 0px;
  float: left;
  position: relative;
  overflow: hidden;
  border: 1px solid black;
  background: #ccc;
}
<div id="post-501" class="post-501 post type-post status-publish format-standard hentry category-moto-dz-films tag-news-sub-2">
  <div class="video-entry-summary">
    video 1
  </div>
</div>

<div id="post-240" class="post-240 post type-post status-publish format-standard hentry category-videos">
  <div class="video-entry-summary">
    video 2
  </div>
</div>

<div id="post-232" class="post-232 post type-post status-publish format-standard hentry category-videos">
  <div class="video-entry-summary">
    video 3
  </div>
</div>

<div id="post-223" class="post-223 post type-post status-publish format-standard hentry category-videos">
  <div class="video-entry-summary">
    video 4
  </div>
</div>