After hunting through the generated html in Print Templates with esri.request example, I found that the generated menu is of type dijit.Menu. If you want to style it, Here's a very condensed version of the html, which will help you reskin it using css. This is by no means a comprehensive list of classes or table structure. It's just a boiled down version to help modify the styling. In this example, the second choice is hovered over.
<div class="dijitMenuPopup">
<table class="dijitMenuTable">
<tr class="dijitMenuItem">
<td class="dijitMenuIconCell">
<!-- image icon probably goes here -->
</td>
<td class="dijitMenuIconLabel">
Letter ANSI Portrait
<!-- label here -->
</td>
<td class="dijitMenuItemAccelKey">
<!-- I don't know what goes here -->
</td>
<td class="dijitMenuArrowCell">
<!-- if a submenu is present, the arrow goes here -->
</td>
</tr>
<tr class="dijitMenuItem dijitMenuItemSelected dijitMenuHover dijitHover">
<td class="dijitMenuIconCell">
<!-- image icon probably goes here -->
</td>
<td class="dijitMenuIconLabel">
Letter ANSI Landscape
<!-- label here -->
</td>
<td class="dijitMenuItemAccelKey">
<!-- I don't know what goes here -->
</td>
<td class="dijitMenuArrowCell">
<!-- if a submenu is present, the arrow goes here -->
</td>
</tr>
</table>
</div>