The problem here is miscommunication. There's a prompt because Fire is using the itch.io desktop app (as I do) and you clearly don't know that exists (as many other devs on here don't either so you're not alone in that). The reason nothing is coming up to install on itch.io is because the game hasn't been set up to work with the desktop app (using the Butler system). As such, until that changes (if it ever does), Fire will need to go to the website, download and install it manually. I hope that helps.