How can I access the windows audio sub system? this is my first time ever hearing of this "audio sub system".
You don't. Not directly. It's just the part of Windows that handles audio. It takes whatever settings you have for it in the general Control Panel and for each device, manages your audio devices, and provides some convenience functions like loopbacks of all the outputs that can greatly help a livestream, environmental effects that kill it, etc.
The reason that a DAW might not use that is because Windows tries to be so smart with it that it ends up being stupid. So the DAW bypasses Windoze's audio system entirely, using an ASIO driver that talks directly to the card. This makes the audio hardware work exactly as expected - as a dumb converter between the DAW and the outside world - but Windows can't see what it's doing anymore and can't loop it back.
(only Windoze needs this; every other system understands the KISS principle and works just fine on its own)
Also the audio coming out of my DAW (pro tools) travels out of my pc through a usb cable to an interface which then processes the signal and then sends it to my speakers via 1/4" cables.
Another question: how do I "resolve" capturing and routing DAW audio output into OBS?
You might be able to have the DAW use Windows' audio subsystem anyway, and then the Desktop Audio loopback should work. You won't get the external processing, but I assume that that's specifically for those particular speakers and not needed for the stream anyway?
That's a setting in the DAW, not OBS. Something like disabling ASIO, perhaps?
And one more quick question: what does "s/w" stand for?
software