get_terms: determine if taxonomy term has children

The get_term_children function should help here.

This returns an array, either with the child terms inside it, or empty. Checking if this array is truthy or not as you loop through will then let you determine whether or not to add the class.

<?php
    $terms = get_terms('wpsc_product_category');
    if ( !empty( $terms ) && !is_wp_error( $terms ) ){
    foreach( get_terms( 'wpsc_product_category', array( 'hide_empty' => false, 'parent' => 0 ) ) as $parent_term ) {
        $term_children = get_term_children($parent_term->term_id, 'wpsc_product_category'); ?>
        <li class="header-menu-item<?php echo ($term_children ? ' parent' : ''); ?>" data-hook="<?php echo $parent_term->slug; ?>">
            <a href="https://wordpress.stackexchange.com/questions/168749/<?php echo home_url(); ?>/products/<?php echo $parent_term->slug; ?>"><?php echo $parent_term->name; ?></a>                
        </li>
    <?php }
} ?>