I've seen a few russian pirated game releases for linux do this, they just bundle a copy of wine (downloaded from the same places as e.g. lutris gets it from), and a start script that sets the WINEPREFIX variable to a pre-populated prefix, with the game already installed and all the needed registry configurations already present. I suppose you could bundle all this in an AppImage, the annoying part however is that the WINEPREFIX is supposed to be read-write, so you'd have to set it to some place specific to your app, to avoid messing with the user's main prefix. These prefixes are huge (hundreds of MB upon creation), so I'm not sure I'd consider this a desireable solution.

If this is your distribution method, consider having the user install wine before running your app.