Blizzard have updated their official 18th anniversary guide to clarify how players can get the two Korrak’s Revenge battleground mounts, as there was some confusion. There were also bugs preventing players from getting the mounts, even with the badges, which may have been resolved since this update was posted just now.
Korrak’s Revenge Mounts (Source)
Return to Alterac Valley of Olde
Run down your enemies, raze their fortifications, and exchange the tokens you loot from their corpses to summon mighty reinforcements in Korrak’s Revenge, a throwback Battleground inspired by the earliest days of Alterac Valley.
Players who participate in Korrak’s Revenge and complete the bonus objective to obtain 200 Timewarped Badges from the event can earn two mounts: the Stormpike Battle Ram (Alliance) and the Frostwolf Snarler (Horde).