What you have makes sense, except that your variable names dont match. You have $object in your function definition and in the function code you are trying to use $order.
Adjusted:
/* SEND ADMIN E-MAIL TO LOGGED IN USER */
/* --- */
add_filter( 'woocommerce_email_recipient_new_order', 'your_email_recipient_filter_function', 10, 2);
/* Add parents e-mail address to new order admin mail */
function your_email_recipient_filter_function($recipient, $order) {
$user_info = get_userdata($order->user_id);
$recipient = $recipient . ', ' . $user_info->user_email;
return $recipient;
}