Ok. When I get home, I will test and write instructions. It will be very simple :) Check back in a few hours and Ill have something for you.
So I'm sorry to say but it looks like it is not possible to fix at this time. All though deprecated, the issue was not with System.Jason.dll.
Digging into it I believe that Itch.io's API endpoint has changed, and the key generated only has access to profile info, not game info. I will follow up with Itch and investigate further.
That's what this plugin uses. The token generated during authentication is used to make the API call https://itch.io/api/1/KEY/me. Once that returns a UserID, another call is made to verify the purchase https://itch.io/api/1/KEY/game/GAME_ID/download_keys.
It seems the last API call mentioned has been updated.
I have made a post on the support forum, this is the link if you would like to follow also. Once I have an update, I can update the plugin.
https://itch.io/t/1114371/itchio-api-endpoint-change