Goal: I'd like to make it as easy as possible to get users to go from my game's webpage to an installed version of the itch app - with my game installed in the app, so the user only downloads one app and doesn't have to search for or download my otherwise unlicensed game, avoiding the scary prompt for newer users. I think this is the best UX and accomplish-able without forcing custom builds of the app thusly:
1. Upload my game to itch.io
2. Have my itch.io page link to a itch.io app installer w/ an argument of my game's ID in the URL that is embedded into the download somehow (filename would work)
3. Use the ID argument to alter the itch.io install process such that after the initial install, the app immediately downloads my game (a user prompt would be fine, they'd be expecting it)
That way the user would never have to search for my game after installing the App, also, if it's the only link to download my game on the internet, there's no way they would get the security prompts that would occur running my game raw.
Biggest question mark on your end is #2 of course -- how do you take the URL argument and have it ready as a string for the installer on the client -- but I think a filename would suffice. The security risk is minimal as it would have to be a valid public ID in your database of games anyway.
Would love to see it!