Shit, sorry, made a mistake. Indeed the game/GAME_ID request returns just general info on the game. Uploads info is https://itch.io/api/1/API_KEY/game/28768/uploads
Viewing post in Download a game with the API
Yeah I think you may have better luck with butlerd
https://github.com/itchio/butler/tree/master/butlerd - basically butler
is a command line interface to butlerd
which is a daemon with JSON RPC interface. I did not try it myself, but the docs seem to be pretty comprehensive https://docs.itch.ovh/butlerd/master/ .
GameHub launcher apparently uses butlerd for itch.io integration https://github.com/tkashkin/GameHub/tree/master/src/data/sources/itch