It looks to be analogue only from what I can see looking on the website. Cannot see any mention of USB, so the Steelseries engine probably works like Razer's software, in that you don't actually configure the headset per se, but the audio output that the headset is connected to.
A headset with analogue connections cannot be recognised by Windows as a device in it's own right, because there is no digital connection for information to be passed telling Windows exactly what has been connected. That's why it doesn't show up in the sound properties as a separate device. It would need to be USB in order for Windows to recognise it as a Steelseries Arctis 3 headset.
With an analogue headset or headphone Windows an only see the audio device that headset or headphone is connected to; whether it be sound card, onboard audio or an external device.
If you get no sound when plugging them into your DG, it's likely that either that isn't set to default audio device in Windows sound properties, or you may have the output on the sound card set to speaker or possibly set to front panel, if you are using the connection on the card itself.