Does Arch Linux have GUI?

You have to install a GUI. According to this page on eLinux.org, Arch for the RPi does not come pre-installed with a GUI. No, Arch doesn’t come with a desktop environment.

How install Gnome on Arch Linux?

First of all, make sure you have updated your Arch Linux system. After updating, reboot Arch Linux to apply the latest updates. This command will install all required applications including the gnome display manager for the GNOME desktip environment. You can, however, use other popular DMs (display manager).