The Gajapatis were a medieval Hindu dynasty that ruled over the region of Odisha (Orissa) in Eastern India. The Gajapati rulers played a significant role in the history of the region, particularly during the 15th and 16th centuries. They were known for their patronage of art, culture, and religion, and their rule coincided with a period of flourishing literature and architecture in Odisha. Therefore, the Gajapatis were associated with the governance and cultural development of the historical region of Orissa.

So, the correct option is [2].