List subcategories of a specific product category (adapting from posts to products taxonomy)

…to show the subcategories of a specific category (ID 89) …

Try this

$product_cats = wp_get_post_terms( $post->ID, 'product_cat' );
if ( ! empty( $product_cats ) && ! is_wp_error( $product_cats ) ) { ?>
<ul>
    <?php 
    foreach ($product_cats as $childcat) : ?>
    <?php if ($childcat->parent == 89)) { ?>
        <li>
            <a href="https://wordpress.stackexchange.com/questions/331894/<?php echo get_term_link($childcat->term_id); ?>"><?php echo $childcat->name; ?></a>
        </li>
    <?php } ?>
    <?php endforeach; ?>
</ul>
<?php } ?>

I hope this helps.