(9/21 11pm) Edit: Blizzard has hotfixed this and now characters 60 and up can get the epic bag.
This might be a bug, as, generally, those “rare reward” bags like Heart-Shaped Box and Loot-Filled Pumpkin are available to characters at the level cap of the previous expansion, which would be any level 60 or above character during Dragonflight.
Items that can drop from Keg-Shaped Treasure Chest include:
Level 60-69 Character | Level 70 Character |