I see, thanks for the reply. I have browser cookies intentionally limited so that makes a lot of sense. I assumed it saved to the itch account for some reason. I'll probably download the game for the future. I have been really enjoying it!
I believe the itch.io app is rather parsimonious with it's cookies, so most of the web versions of games you play through the app will not do a good job of saving data in cookies... can't confirm but I don't have any problems using it to install web games and then losing data so I'd recommend doing that! (They're usually pretty small after all!)