Hi, I opened an issue on the github page with similar proposal (including matchmaking): https://github.com/itchio/itch.io/issues/500
This would be an incredible feature. A documentation for such system wouldn't be so complicated if everything is returned as a JSON (or any other simple file to parse).
I imagine that each application (game) would need a App key to make such requests, too.
Edit:
Requests could be done using any URL transfer library (of the game developer choice, take cURL as example), so the itch.io developers wouldn't need to create a client-side API, only the server side, that would provide informations such as who is currently playing the game (so matchmaking would be possible), which are their achievements and scores (in-game content).