Refund denied

Hey - when reviewing my credit card statement I realized that my 10 year old had purchased multiple gem packs in the game Rise of Kingdoms.

I requested refunds, using the “purchased by minor child” option for reason for request. All of the large dollar purchases were denied and I am out $100s of dollars. Resubmitted the claim and was denied again. Am I missing some your am I out of luck?

thanks for any feedback!