Can You Play iMessage Games on Android?
No. iMessage games only run inside Apple's Messages app, so Android phones can't open them.
Why not
iMessage only runs on Apple devices, and iMessage games run inside iMessage. When you text an Android phone, your iPhone uses RCS or SMS instead (green bubbles), and neither supports games.
That applies to whole group chats: one Android phone and nobody in the group gets games.
Game Pigeon has never been released for Android, so skip any “Game Pigeon APK”.