Would that not be handled by some kind of launcher? The launcher checks if stuff needs to be installed and acts accordingly.
The launcher can be the game itself. But this is stuff that I would not expect from a game I got from itch. Also bad for building for different targets from one source.
If we talk about a real creation tool, maybe. But even then, you can have the user associate the file extenstion if desired. The app does not need this to operate.
This is still a recreational app we are talking about, is it not? Also known as a game.