How to query all custom posts of a certain type and checking what category they have

Alright I figured it out!

$args = array(
'post_type' => 'vendors',
'order' => 'asc',
'orderby' => 'title',
);
$query = new WP_Query( $args );
if ( $query->have_posts() ) {
echo '<ul>';
while ( $query->have_posts() ) {
    $query->the_post();
    $category = get_the_category();
    echo '<li class="';
    echo $category[0]->category_nicename;
    echo '">' . get_the_title() . '</li>';
}
echo '</ul>';
} else {
// no posts found
}
/* Restore original Post Data */
wp_reset_postdata();