One is a Dell 2408WFPb and one is a Gateway FPD2485W
Thank you for that information.
I double check the specs for your monitors and noticed that the reason why you are unable to get audio through HDMI is because none of the monitors have a built-in speaker. Actually, both of them provide an optional speaker bar; therefore, the Intel® NUC is unable to list them as Playback devices.
Check the specs here: