Convert all dates stored in custom field

Find the correct key for game_date_key and run this once:

global $wpdb;
$posts = $wpdb->get_results("SELECT ID FROM ".$wpdb->prefix."posts" WHERE post_type="post");
foreach ($posts as $post) {
    $old_date = get_post_meta($post->ID,'game_date_key',true);
    $new_date = date('d/m/Y', strtotime($old_date));
    update_post_meta($post->ID,'game_date_key',$new_date,$old_date);
}

(I assume you will have the sense to backup your database first just in case. 🙂