Explanation:

- The sentence talks about the role of Mamallapuram in the context of China's ancient Silk Route.

- Option 1: Intentional - This implies a deliberate or purposeful part, which doesn't fit the context well, as the focus is on the importance or essential nature.

- Option 2: Integral - This means essential or necessary for completeness, making it the most fitting choice here.

- Option 3: Intuitive - This implies being based on intuition or instinct, which doesn't align with the historical and factual sense required.

- Option 4: Intensive - This suggests involving a lot of effort or activity in a short period, which doesn't properly describe Mamallapuram's role.

Given these explanations, Option 2, "integral," is indeed the best choice.