How to display class name in this shortcode post query

OK, so you have to modify some part of your code like so:

$list=" ";

while ( have_posts() ) {
    the_post();

    $terms = get_the_terms( $post->ID, 'port_tags' );
    $terms_string = '';
    if ( $terms ) {
        foreach ( $terms as $term )
            $terms_string .= $term->slug . ' ';
    }

    $list .= '<li class="mix all '. $terms_string .'">' 
    . '<div class="listing-content">' 
    . '<h3><a href="' . get_permalink() . '">' . get_the_title() . '</a></h3>' 
    .'<p>' . get_the_excerpt() . '</p>'
    . '<a href="' . get_permalink() . '">' . 'View &raquo;' . '</a>'
    . '</div>'
    . '<a class="listing-thumb" href="' . get_permalink() . '">' . get_the_post_thumbnail($page->ID, 'listing-thumb')  . '<span></span></a>'
    . '</article>';  // <- it should be </li> not </article>, I guess - you don't open any <article> tag in this loop
}