He was teleported 30 years ago, to an alternate timeline where the horde was forming, but still hadn't partaken in the demon blood, or replaced all shaman with warlocks.
We get teleported 28 years ago to that same alternate timeline, so Garrosh has been there for two years already making changes to the past.
Actually no. Cairne was wiping the floor with Garrosh's face during the entire fight. Garrosh was only able to land 1 lucky strike that barely managed to scratch Cairne, but since his axe was poisoned (without him knowing it) that scratch managed to paralyze Cairne, leaving him open for garrosh to cleave him in two.
Before he got that lucky scratch however, he was fighting as hard as he could and wasn't doing anything at all to Cairne, whereas the old bull was absolutely pummeling Garrosh and wasn't even tired.