The headset connects to your PC or Xbox One using a 3.5mm jack, though you'll need to use Razer's Audio Enhancer (which is included) and plug it into a USB port to use it on PS4. The USB converter works on PC too, letting you plug in two headsets if you prefer to stream with a friend or your significant other -- it's compatible with any 3.5mm headset.
Razer is taking a different approach here, in emphasizing streaming aesthetics, perhaps at the expense of richer game audio. The product page doesn't discuss earbud quality in much detail, so if you typically play games where directional audio is important, for instance, a more typical over-ear setup might work better for you.
Still, Razer's latest offering could be a solid option if you don't want to use earbuds and a standalone mic, but still want to showcase more of your face to foster a more personal connection with your audience on streams. Ifrit costs $100, and you can pick up the USB Audio Enhancer by itself for $20.