Windows can output to as many sound devices as you can physically attach, provided the software used to output the sound can specify which sound device to output to.
The problem is that, most games and general use software is only written to output to the default sound device.
Software such as Windows Media Player, VLC, and commercial media playback software allows for the user to specify which audio output to use. Since you can't rely on your games to give you an audio output selection, expect to set your default audio device to whatever you want the game to use as it's sound source. I would assume the motherboard audio or a sound card should be sufficient for gaming. Most decent media playback software can target a specific audio device, so personally I would shoot for HDMI audio out through the display's speakers, for the media playback. Since primary focus will be on the games being played, I tend to use the better audio output, such as through amplified speakers for that, and the half ignored audio I relegate to the inferior display speakers.