I don’t know the status for arch Linux. On many Linux distros the GUI is in a separate package, e.g., swi-prolog-x (x for X11, which is no longer used).
The GUI surely used to be there for arch. It might be relevant that SWI-Prolog 10 gui is no longer based on Xlib, but on SDL3 and SDL3 is only around in the latest release of many Linux distros. I’d expect arch to be one of them though.
So, I think it should be possible. Let us know. If all fails, you can also try the flatpak. That should run on any Linux system, with it without SDL3.
That is not very clear Is the GUI not installed or does it not work? Try (in swipl)
?- check_installation.
That should tell you something about the configuration and installed components. And no, Wayland should not be a problem. My main platform is Fedora 43, which is Wayland-only (well, with XWayland for running X11 applications. XWayland caused some issues before the migration to SDL3).