Ok, here's the deal. I have looked online quite a bit, and I can't find anywhere that actually says how to do this. Just that you shouldn't (for reasons that do not apply to me, more on that below). You can skip straight to my question at the bottom, however clarifications/explanations/etc. will be divided up before it, so here goes.
I am currently using a G933 headset (soon to be G935) in stereo mode, with Dolby Atmos for Headphones enabled on my PC. This is fully compatible with Dolby Atmos, 7.1, 5.1, etc. Please note, I am not using any kind of surround sound speakers. The surround sound is virtualized for a stereo headset. Windows 10.
What Research I've Done
I've done quite a bit of Googling on the situation, but my Google-fu has failed me. Everything I've come up with has said not to do this because you need amplifiers, etc. to power the speakers. I don't need that as I am using a virtualized headset.
My Audio Sources
The sources of my surround sound will be mostly consoles like the PS4, Xbox One, Wii U, etc. as well as things like Amazone Fire TV. I will be using an HDMI Matrix with six inputs and two outputs to hook them up to my monitor. Its sound outputs are through the output HDMI, an optical SPDIF output, and an AUX cable output.
What I've Tried
I have tried using my Elgato capture card to receive the 5.1 surround sound from the Wii U via HDMI, but even if I could do it without capture software open, it only comes through with stereo (3/5 dings are heard on the audio test: left, right, and center).
How can I get surround sound audio (including, but not limited to, 5.1/7.1/Dolby Atmos) from an HDMI cable (or any other cable) into my PC? I don't need my PC to be an AV Receiver in the "Home Theatre" sense (I'm not powering a bunch of speakers). I just need to be able to input the surround sound to my PC in such a way that Dolby Atmos for Headphones can receive it as surround sound and as such, output the surround sound virtually to my PC headset.
I tried to include everything I can think of, but if I should add more info let me know. I appreciate the help.