Do you mean this one?
game:view:ownership
curl -X GET "https://api.itch.io/games/GAME_ID/ownership" -H "Authorization: Bearer ACCESS_TOKEN"
Yeah the way I understand it, it only shows ownership of the game with GAME_ID, and the user needs to have authenticated with the oauth flow, because they need the ACCESS_TOKEN.
But it does show you if the given authenticated user owns the game that is specified with the GAME_ID.