Is it possible to output different audio to HDMI and built-in speaker simultaneously?
You could try using AirFoil. I use it on my Mac to send audio out from a specific application to multiple sources (which can include the internal speaker as well as any external audio output device).

My use case though is to allow Spotify to send its audio out to my AirPlay speaker while allowing the internal speakers to still play only system notification sounds.

Check it out here: https://rogueamoeba.com/airfoil/mac/

(note I do not work for AirFoil, just an awesome product).