first i assume you are talking about DEs (desktop environments) and not window manager, since MATE is a full desktop environment and not a window manager.
(to explain it a simple way: window manager are just responsible for the frames around your applications... like Compiz, Metacity, Marco, etc.)
as you pointed out you need a ARM-build for a ARM-CPU, x86-build for a 32bit-CPU and so on...
usual a SBC (single board conmputer) has not enough "graphical power" to run a DE which needs 3D-acceleration like Unity (the default ubuntu DE) or GNOME 3.x.
for sure your ARM board may have enough power to run a ubuntu-system (so there is the possibility to provide a MATE-built), but that don't have to mean also the default or every other packaged graphical desktop environment!
maybe i am wrong and you can try to install unity afterwards with the command sudo apt-get install unity
, but i'm pretty sure that won't work and you will mess up your system.
first backup your files and expect you have to reinstall ubuntu!!! -- don't blame me that i haven't warned you!