Based on this output, I think you'd need to set in EmulationStation the Audio Card to Device.
To get the name of the mixer (volume control), run
amixer scontrols -c Device
and choose the 1st entry and set it as Audio Device. For instance, in my case, the USB audio card is named 'Controller':
amixer scontrols -c Controller
Simple mixer control 'PCM',0
Simple mixer control 'Headset',0
I would use PCM as the AudioDevice settings in ~/.emulationstation/es_settings.cfg:
<string name="AudioCard" value="Controller" />
<string name="AudioDevice" value="PCM" />
This should fix the audio not working (or the volume slider rather) in EmulationStation.
For Amiberry, I'm not sure why it's not working - maybe it's trying to use the 'default' card and it's not working ?
Try following the advice here and create a /home/pi/.asoundrc file containing
defaults.pcm.!card 1
defaults.ctl.!card 1