Yes, and that is deliberate. You do not need an account to order or to track your order.
Without an account
Go to Track order and enter two things: your order number, which starts with ORD- and is in your confirmation email, and the email address you ordered with. You then see the status, the expected delivery, track and trace if available, and your invoice.
Those two details are also the check. Without both we show no order details, not in the chat either.
With an account
You can create an account. It helps if you order regularly: your orders are kept together and your address details are saved.
Lost your order number
Search your mailbox for the confirmation email sent right after payment; the number is in there.