How to show custom taxonomy child posts through shortcode in WordPress

That is a very messy shortcode but it looks like if you pass a term slug into the shortcode cat att this part…

if (of_get_option('shortcat_video', '1') == '1') {
    $query = array(
        'posts_per_page' => $items,
        'orderby' => $orderby,
        'order' => $order,
        'post_type' => 'video',
        'tax_query' => array(
            array(
                'taxonomy' => 'videos',
                'field' => 'slug',
                'terms' => array(
                    $cat
                )
            )
        )
    );
}

… would display those videos, except that the of_get_option conditional may be preventing that block from running. I don’t know what that is or how it gets set. And since I don’t know what that conditional is for I can’t say what the result would be if you remove it. That tax_query component is what you need though.

If passing that slug doesn’t work you probably need to create your own shortcode, which you could do by copying that one and altering the top part. Let me know if you need to do that and need help.