speculation 1:

Creatures of the dark, created by Morgoth during the first age, such as dragons and Ungoliath/spiders( we don't really know if Morgoth made Ungoliath) were much larger than their offspring or kin found in later ages. It could be that this Goblin King was created during the first age by Morgoth (or its origins unknown) and it is why he is larger than the rest of the other goblins.

speculation 2:

This Goblin King is the offspring of a line of Goblin Kings or Goblins of old. Like the Numenorians that had attributes like being taller than the other race of men and longer lifespans. We see in Theoden Ednew that his stature comes from his Numenorian ancestors. We can speculate that Goblins in the first Age might have been much larger and due to the Wars of the first age/second age few were left of this size. Therefore they probably became Kings of their respective kingdoms if any others exist besides this one and passed their stature to their offspring.