Is the seller obligated to refund the money to the buyer whose game account was banned due to the use of unauthorized software, or does the buyer bear the consequences of his actions?

If the buyer caused the game to be banned due to misuse and it had no defect, then nothing is incumbent upon you. However, if the game was defective at the time of sale, then the buyer is justified in requesting a refund and you are obligated to return it; as Ibn Qudamah mentioned, if the buyer discovers a defect that he was unaware of at the time of purchase, he has the option to either keep the item or cancel the transaction. It should be noted that whatever is permissible to play with is permissible to trade, and whatever is forbidden to play with is forbidden to trade.