Not sure, how you would get chrome to cooperate on tab level without actually having configuration options in chrome.

On windows it's usually "default device" that apps look for, so switching a default device to one card, starting an app and then switching the default for next app may work, but it sounds incredibly annoying having to do that every time. On top of that, the app may look for the default device every time an audio stream starts playing, so essentially you would have to have the right device as default every time you click play or unpause in that particular app.

I have managed to split a single 5.1 audio card into separate 2+2 stereo channels under linux for multi-headed configuration, but yeah.. Having the default for web browser and finding a music player, that lets you choose the output device would be my first guess. But good luck with actually trying to split single audo device like that under windows. Having USB headphones, that are essentially a USB sound card + headphones might work much easier.

Probably some sort of virtual sound card, that then lets you configure the physical outputs would work under windows, but does something like that exist?