EmulationStaton doesn't need sudo to run and never has.
We don't support DietPi on the Pi, so I'm not sure you're using the RetroPie main repository or some fork that supports DietPi.

@fenris RetroPie is not supported on any Raspberry PI distro out there - check the docs. For instance, DietPI does not have the graphics stack installed and therefore it's not suited for RetroPie.

I'd advise to start by trying the pre-built images on the RetroPie download page (which are based on Raspbian Jessie Lite image) and see how it performs.

NES games should work fine on a PI Zero-W, but for SNES I'm not so sure - others may chime in.