Garruk was never hunting Liliana for sport. He briefly hunted her because she killed one of his beasts, and then hunted her because she cursed him.
Having heard of a huge predatory creature called the Ursoth on the plane known as Shandalar, Garruk planeswalked there and hunted the Ursoth with the help of his summoned beasts.[6] When another planeswalker, by the name of Liliana Vess, killed one of his beasts he flew into a rage and tracked her down, assaulting her in an ancient Onakke temple. The ageless necromancer was initially over-powered by Garruk, forcing her to use the artifact known as the Chain Veil she'd been sent to claim from the temple. Using the Chain Veil, Liliana overpowered him with a surge of black magic that cursed him, warping his summoning powers and wracking his body.[7]
I misremembered the curse as happening on Innistrad rather than Shandalar. I guess he just tracked her to Innistrad after she cursed her. (In my defense,
Garruk Relentless implies a different story, but we can set that aside.)