There is no way to do this automatically, at least without putting in some work to reconfigure the video editor and the program.
The underlying goal and features I think you'll be (creatively) utilizing are the Windows Communication Monitor (I don't know what else to call it), to adjust the volume of all other programs when your video program makes noise.
Open Audio Devices and Sound Themes by clicking the Start button, clicking Control Panel, clicking Hardware and Sound, and then clicking Sound then clicking on the communications tab.
Then choose the volume reduction level (eg. 80%).

What you'll need to do is essentially this:
- Download and install a virtual speaker or sound card. (search Google for VSC or something similar to find VSC software. I stumbled upon Virtual Audio Streaming, which might just do the trick.
- Configure your video editor to use the virtual speaker as the default playback option.
- Download and install a virtual audio cable (optional if the VSC or similar software can automatically route the audio stream). A simple Google search turned up Virtual Audio Cable.
- Download and install a virtual microphone.
Send the audio from the VSC (step 1&2) to the virtual microphone (step 4).
after you've done all this...
Open Sound by clicking the Start button , and then clicking Control Panel. In the search box, type sound, and then click Sound.
Click the Recording tab, click (the virtual)Microphone, and then click Properties.
click the Listen tab, click the Listen to this device check box, ensure that the playback through this device is set to your real speaker and then click OK.
What should will happen is the sound from the video editing program will be perceived as communication, so Windows will automatically reduce the volume of all other programs (internet browser for example, with your music stream), and you'll be happier.