I have an Intel Pentium G4500 on a Fujitsu Mainboard D3474-B (Thin-ITX) and when i open Kodi and go into System Settings, Audio, Audio Output Device i choose "HDA Intel PCH, SAM SyncMaster (that is my TV connected via HDMI) on HDMI #0".
Then i have sound within kodi.
I exit kodi and go to Batocera ES Menu, System Settings, Audio Output and choose: "HDMI0 PCH [HDA INTEL PCH]" and then i have sound in games also.
This method always worked for me (and i have tested plenty of different PC Hardware).
What exactly do you see in Kodi Audio Output Devices? Could you make a screenshot of the devices listed there?
And then also a screenshot of the list of audio devices in Batocera ES?