Can I display custom plugin categories w/ normal categories on homepage?

I am using the Arthemia theme (https://bit.ly/140wf) which has a Categories bar beneath the headline/featured posts (look here). It displays the category & description.

To set which categories display here, I simply the following lines in the index.php file to match my desired category IDs:

<?php $display_categories = array(5,6,15,8,9); $i = 1;
	foreach ($display_categories as $category) { ?>

	<div id="cat-<?php echo $i; ?>" class="category">
		<?php query_posts("showposts=1&cat=$category")?>
		<span class="cat_title"><a href="<?php echo get_category_link($category);?>"><?php single_cat_title(); ?></a></span>
		<a href="<?php echo get_category_link($category);?>"><?php echo category_description($category); ?></a>

My problem stem from a plugin that I am also using, WP Business Directory Manager (https://bit.ly/c0rLpJ). It uses custom taxonomy/categories to organize directory listings and I would like to display one of these categories on the homepage with the traditional post categories. The plugin categories follow the same ID structure as traditional categories and do not overlap ID #s with traditional categories… so why shouldn’t this work, right?

Visiting my site here you can see that the theme displays a blank box in the Categories bar instead of showing the name/description of the category from the WP Business Directory Manager plugin.

Does anyone know why this happens, or how I can fix it?
Is this possible?
Do I need to modify code from index.php or within the directory plugin?

Any help is greatly appreciated.