Was this feature ever implemented?
Yes. You can create a new source for the application with the audio you want to capture.
Technically yes. Use the Application Audio source or whatever it's called. However, I don't use it myself because of some problems with how it has to work with the operating system. For some apps it works, for others it doesn't. I want something that *always* works.
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So I still fall back on the old-school-analog mindset of having an obviously-separate path for each thing that I want to keep separate, and an explicit mixing step. In this case, that would involve having multiple sound cards or audio devices. They could be physical or virtual, so you don't necessarily have to buy any more hardware, but either method works.
Send the game to one of them and everything else to a different one, and then Desktop capture (Settings -> Audio) or Audio Output capture (in a scene) the one you want.
If you want to have both in your headphones, then you'll need physical cards and physical wiring, because the computer will no longer output everything on one plug. Or you could be careful with OBS's Monitor...
Or, you can try something like VoiceMeeter:
VoiceMeeter Banana, the Advanced Virtual Audio Mixer by V.Burel
vb-audio.com
VoiceMeeter Potato, the Ultimate Virtual Audio Mixer for Windows
vb-audio.com
Two different sizes of the same thing, as a mixing console that comes with its own virtual sound cards. Connect something (like the game) to one of those virtual speakers, and it appears as an input to VM. Connect something (like OBS) to one of those virtual mics, and you can feed it from VM.
VoiceMeeter can also connect to physical devices, like your mic and headphones, so that ALL of your audio work can be done in that one place.
Not everyone likes VM though, because most signals have to take at least two separate trips through Windows' audio system. Depending on your rig, even one trip might be slow enough to notice, let alone two!