As active Linux desktop user I can tell I see the AppImage format quite often. Even some tools here on Itch use it. Tiled for example ports as AppImage. But I have no idea how it handles package dependencies. If you like to play it safe, distribute your game as deb or rpm package as well as a tar.gz archive (for the less popular distros). If possible, include a readme in the tar where you list up all your deps and requirements. I think you basically got it covered well enough that way.
Thank you for your time. The dependencies I work with now should be rather common (zlib and SDL2, (plus SDL2_Mixer and SDL2_Image)), but since I do not know what the future brings. Linux ports are not even a promise yet, but a friend of mine who is a real geek (and he even takes pride in that, so I can safely say that) did already say he'd help me when the time comes. Yet I do see that AppImage can still be a good way to go to make sure "nothing can go wrong"... well it sounds at least most "fool-proof" to me, at least for the itch app. A deb/rpm may still be an option as separate download for the more "purist Linux user" I guess... ?