Users need to add a PPA to Ubuntu MATE 15.04
As it stands right now, Ubuntu MATE comes with support for two windows managers, Marco and Compiz. Due to popular demand, the developers are also working to bring support for Mutter and Metacity, and a PPA is already available.
There aren't too many Linux distributions out there that feature not one but two windows managers included by default. Ubuntu MATE has Marco as the default solutions, but the OS also has Compiz installed. It's only a matter of changing the favorite one from the system settings.
From the looks of it, the community has been asking developers to provide support for another two famous windows managers, Mutter (from the GNOME stack), and the old and trusty Metacity. They will be better implemented in the future, but for Ubuntu MATE 15.04 users just need to add a PPA and run a few simple commands. It might sound a little bit complicated, but if you're interested in changing something like the windows manager, then you probably also love the terminal.
Ubuntu MATE team is listening to the community
Not to say that other Ubuntu teams don't do the same thing, but the Ubuntu MATE team seems to be paying really close attention to what users want and they don't wait months or years to implement those features. If it doesn't cause any problems and it can be done with a reasonable amount of work that doesn't rob developers of too much time they would otherwise spend on the next iteration, then it's going to get added.
Users will need to upgrade MATE Tweak, so open a terminal and enter the following commands:
sudo add-apt-repository ppa:ubuntu-mate-dev/vivid-mate
sudo apt-get update
sudo apt-get dist-upgrade
Users have to logout and log back in, after which they enter these commands as well (just like the previous one, root is needed:
sudo apt-get install metacity mutter
sudo apt-get install ubuntu-mate-libreoffice-draw-icons ubuntu-mate-libreoffice-math-icons
You will find the new windows managers in the list, in MATE Tweak. That's pretty much it. Many thanks to Martin Wimpress for providing the instructions on such a short notice!