dnf groupinstall mate-compiz (I got this by running
dnf grouplist -v). That will install all of the packages that are part of the MATE desktop environment, rather than just the
mate-desktop package, which (even tithe name suggests more) is just this:
Name : mate-desktop
Summary : Shared code for mate-panel, mate-session, mate-file-manager, etc
Description : The mate-desktop package contains an internal library
: (libmatedesktop) used to implement some portions of the MATE
: desktop, and also some data files and other shared components of
: the MATE user environment.
You may also want
dnf groupinstall mate-applications.