The Cool VL Viewer can run just fine under
any "recent" (4-5 years old or less, due to minimum glibc and libstdc++ versions requirements) Linux distribution.
But for best results (performances, stability, features such as copy/paste to/from other apps), just make sure that you can start your desktop suite under a
genuine X11 session...
So, whatever the Linux distribution, do choose a desktop suite running (or capable to run) under
X11: the viewer is a genuine X11 application, and while it
may run under Xwayland, you would suffer from bugs and shortcomings in the latter.
Under Linux, you have a broad choice of desktop suites:
GNOME (now X11-hostile and trying to shove
Wayland down your throat),
KDE (probably the most Windows-alike desktop suite),
Xfce,
MATE (a fork of GNOME 2, that I am using myself), and many other less widespread desktops (LXDE, LXQt, IceWM, Enlightenment, Fluxbox, Openbox, ROX Desktop, Window Maker‍, etc), among which, for Linux Mint,
Cinnamon (a fork of GNOME 3).
And if you are not happy with the default desktop suite coming with your distro, you can always install another (GNOME, KDE, Xfce and MATE are usually always available on Linux distros), or several others, and pick up any of them at each new login.
That's the beauty of Linux: choice and freedom for everything !
EDIT: and I just installed a Linux Mint VM to check: Cinnamon comes configured for X11 out of the box, so no worry about it.