I've heard of people having problems with the game audio capture or application audio capture. Good concept, but it just doesn't work a lot of the time. Don't know why.
It seems to work better to use a loopback instead. This one seems to be the most popular:
VB-Audio Virtual Cable and App's
vb-audio.com
Install that, and you have a new virtual speaker and a new virtual mic. Whatever you send to that "speaker" goes nowhere except to appear in that "mic", but they act like physical devices as far as anything else is concerned. So you go to the game settings and send it to that "speaker", and you set up an Input Capture in OBS that connects to that "mic".
Or, if you already have the game going to some speakers or headphones or whatever, then you don't have to install anything. Just use the Output Capture source in OBS, and connect it to the same device that the game is already going to. You'll also get everything else that goes to that device, but if it's only the game anyway, then it's fine.
If you need to separate things and route different things to different places, then you're back to installing something. If you tab over from the link above, you'll get these:
VoiceMeeter Virtual Audio Device Mixer by V.Burel
vb-audio.com
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
Those are three different sizes of virtual audio mixer, that include 1, 2, or 3 virtual inputs and outputs depending on which one you get, in addition to the physical devices that it can connect to. If you do that, then you can have an Input Capture in OBS connected to a virtual out of that mixer, connect the game to a virtual in of that mixer, and then use the mixer's routing buttons to send the game to wherever you need, both physical and virtual.