Basically:
Home URL - <?php echo $this->url(''); ?>
Downloads - <?php echo $this->url('downloads'); ?>
etc.
Keep in mind the name of your module goes in between the ' '.
So that it's like this:
<?php if (!empty($menus)): ?>
<?php foreach ($menus as $menuItem): ?>
<li>
<a href="<?php echo $menuItem['url'] ?>"><?php echo htmlspecialchars(Flux::message($menuItem['name'])) ?></a>
</li>
<?php endforeach ?>
<?php endif ?>
Basically removes the category's title and just adds the category links without the dropdown.