I just installed Ubuntu MATE 16.04.1 LTS in a VM and everything seems to work fine
For example, SAFE Launcher v0.9.3 and SAFE Demo App v0.6.1 work fine. The latest versions (SAFE Launcher v0.10.0 and SAFE Demo App v0.6.2) also work fine.
So I’m not sure why it wouldn’t work on your machine. Can you give more details on the hardware you’re using maybe? (e.g. CPU, RAM, etc.)