This is Cat Island. It is located in Tashirojima which is a small island in Ishinomaki, Miyagi, Japan. With a population inhabited by mostly cats.
This scene gets a lot better when you learn that it was improvised. They were supposed to share a long hug, but as Shrek picked Shadow up, he realized the characters just wouldn’t be fulfilled unless they demonstrated their love for each other. Shrek went in for the kiss and Shadow reciprocated perfectly, creating the most passionate love scene in cinematic history.