Where is the secret rugby game in Google Doodle?

The Doodle was removed on 6 September 2021 by Google but can still be played in Google Doodle archives.

Momo appears in Doodle Champion Island Games Begin! as a talking NPC, she can be found in the final side-quest in a whirlpool located at the Archery Section. She is implied to be the real Trophy Master. Momo has several references in the Halloween 2022 Doodle.

The Trophy Master is a crane who looks after the trophies in the Trophy House in Doodle Champion Island Games after Momo left the island.

Why can't I leave the Island? You have to get all the scrolls (complete all the main minigames) and complete all the quests to be able to leave the island.