This can be tricky as the the full OpenGL driver (required for Minecraft Java Edition) has never been compatible with the old Broadcom driver + dispmanx.
The most straightforward way to fix Minecraft Pi Edition is to switch Ubuntu MATE back into the legacy Broadcom driver. Run
sudo raspi-config to select the legacy driver then reboot. MATE 16.04 still keeps the names
libGLESv2.so and has a rudimentary launcher in /usr/bin, so then run:
Unfortunately with this approach you can't swap between Minecraft Java Edition and Pi Edition without rebooting each time.
If you'd like to solve that: The Raspbian guys installed a load-time wrapper and switcher script. It's a lot to explain how it works but perhaps could you find a Raspbian Stretch image and copy over
/usr/bin/minecraft-pi along with
/opt/minecraft-pi/lib/ ? Edit: You'd also need to
sudo apt install libegl1-mesa-dev libgles1-mesa-dev libgles2-mesa-dev, and if there are any conflicts here you might need to work around it using
apt-get download with local copying. Furthermore if the wrapped run is still missing a function or two--typically glAlphaFunc()--you must also modify the script to inject
LD_PRELOAD. This workaround is hard enough for Raspbian and even trickier on Ubuntu MATE!