@leejsmith @Twitch0815
The AMD driver download at http://support.amd.com/en-us/download/embedded?os=Linux x86_64 will not work on Ubuntu 16.04
AMD's proprietary Catalyst driver (called fglrx) is not compatible with the Xorg shipped in Ubuntu 16.04 or later. AMD are no longer updating Catalyst for Linux so this proprietary driver is no longer an option.
The only option available is to use the open source driver (called radeon) which is already included.
There is a newer AMD driver framework upstream (called amdgpu) which has both open source and proprietary options, but it does not support the older HD8000-series in the Gizmo 2 (nor does it support the HD6870 I'm running in my desktop PC).
The free radeon driver used to be fairly terrible, but it's quite good these days. Current performance on the Gizmo 2 (and my PC) is as good as it's going to get on Ubuntu 16.04 onwards.
The only way I can see to maybe get better performance is use Ubuntu 14.04 LTS and the proprietary embedded driver linked above, but I don't know if that's possible with the Gizmo 2, nor if RetroPie will still compile on older Ubuntu releases.