OK here's what I think you need to do, let me know if it's still not working: instead of launching in the itch app, find the file location and open "untitled.html" from there. It should hopefully open in your browser. :)
This did work! Other HTML5 games can be installed via app, so I don't know what's going on here -- the app makes it look like there aren't any builds of Felicity. Maybe you need to specify that it's an HTML5 game, somehow?