Hey there,
Does that work for you? https://github.com/itchio/butler/commit/a46969012a3bd3f0ef48ea7d54f9f6750ec1387e
You're right, I doubt passing ITCHIO_GAME_PID would be general enough to be justifiable, and implementing the Presence API ourselves would be a good idea. Feel free to open an issue at https://github.com/itchio/itch/issues