Yes, the fraudsters used your credit card information to purchase subscriptions to the service (free shipments.com). The merchant is probably using an automatic billing updater to maintain current subscribers. When the bank changes the account numbers, the Payment Network Operator (Visa, Mastercard, American Express etc.) is automatically updating the merchant with the new account numbers and the billing continues.
Have you gone through the cancelling of subscriptions with the support team at the merchant? Have you contacted them via phone and discussed the issue with them? Have you requested they search their system for subscriptions by payment method?
Your bank may need to contact the PNO for your card, explain the situation and request the PNO no longer update the accounts if the merchant can’t cancel the subscriptions.