Starting with Vista, every program that outputs sound has the ability available to it through Windows to send the sound to a unique audio device, provided multiple audio outputs exist of course. However, it is still up to each individual application that is outputting audio to expose that functionality to the user, and it's not always trivial for developers to add this feature. If the feature is not available in your software, you're pretty much out of luck as to steering your audio output, outside of choosing what your default audio device is.
With DVD playback software and Windows Media Player, you should be able to select what device is used for audio output, or leave them at their normal settings of using the default playback device, as for others, it's going to be on a case by case basis.
My suggestion in your case is, since you likely can't steer the audio as you desire by means of your programs, start your GF's media playback through YouTube, Netflix, or whatever else, having it come out through the HDMI as you normally would, then without interrupting the playback of her video, switch the default audio device on the computer to what you want newly started applications, such as your game to use. After selecting the new default audio device, start your game. Since your media playback through your browser, Netflix app, or media playback software has already generated a software mixer through your HDMI output, it should remain linked to the HDMI output until such time as it asks Windows to create a new, internal software mixer for it (usually when restarting the program), at which time it will likely do so using the default audio device again. This is hardly a permanent solution, but it may offer a work-around for your unusual needs.