PureOS is based on Debian, Qubes is mostly based on Xen (a hypervisor). So when you install Qubes you are essentially installing a custom Xen version with added goodies. PureOS on the other hand is just a plain operating system like what you are used to. Xen is what provides the isolation between the different Qubes. I haven't tried it, but most likely you ...
Download latest release: https://web.getmonero.org/downloads/
With Dolphin (Popular file manager):
Right click the .tar.bz2 and click Extract -> Extract archive here
Find a new folder called monero-gui-v0.XX.X
Open it, and double-click monero-wallet-gui. You're done!