Sorry, have no experience with itch.io app. I use itch.io mostly for demonstration purposes. I'd recommend playing the game on dryadquest.com or download an offline version (can be found on patreon.com/dryadquest)
I've got the same problem now, after downloading version 0.10.0 via the itch app. I'll switch to the offline version, but would lose a big chunk of progress since I cannot access my savegames. Can you tell me where those are stored, so I can copy paste them?
That's good to know, but... when I launch the game via the itch app, it neither uses Opera GX nor Firefox to play the game. It seems to be some integrated browser. And I have zero clue where that one has its local storage