Rewrite rule for post as a child of a CPT

In addition to setting has_archive you need to set rewrite when you define the CPT. I replaced $archives because your code snippet does not have it defined.

$rewrite = array('slug' => 'my-cpt-type', 'with_front' => false);
$download_args = array(
    'labels'            => $labels,
    'public'            => true,
    'publicly_queryable'=> true,
    'show_ui'           => true,
    'show_in_menu'      => true,
    'query_var'         => true,
    'rewrite'           => $rewrite,
    'capability_type'   => 'product',
    'map_meta_cap'      => true,
    // Set has_archive to the prefix you want, so the archive is in the right place
    'has_archive'       => 'my-cpt-name/news',
    // Also set rewrite to the prefix you want, which will affect individual posts.
    'rewrite'      => 'my-cpt-name/news',
    'hierarchical'      => false,
    'supports'          => array( 'title', 'editor', 'thumbnail', 'excerpt', 'revisions', 'author' ),
);
register_post_type( 'my-cpt-type', $download_args );

You will want to:

1. unregister_post_type(‘my-cpt-type’); to unregister the CPT, otherwise WP will not honor your changes. You will not lose any content when un-registering, it just clears the permalinks.

2. Re-register using the settings above, then visit your Settings > Permalinks page to flush rewrite rules. You should then have the structure you want – just be sure to clear your browser cache before you try hitting the new URLs.