The missing document is the delayed confirmation receipt which you say you eventually received. That is your receipt for the payment and you then have the folio from the property. Those two together are the proof of payment.
Don't attempt a chargeback here. Some CC issuers view that as fraud. You paid the correct rate, stayed at the property and have a receipt.
You simply may not have provided the correct paperwork to the accounting folks or they may not be the brightest.