What do they specify those ratings for? For recording video?
I can sort of see why they specify a mid-end gaming graphics card for this, as video encoding is something different to video decoding (which any GPU can do). If you would want to do on-the-fly video compressing I could see how things get very slow. Compare the rendering time of a Full HD video to the video length, if that ratio is greater than 1, your render takes long than the footage, and is not able to keep up. Especially at 60Hz, which means you need double the power.
However, streaming video data is something about the USB3.0 support/capability and writing it to a harddrive. That has nothing to do with GPU or even CPU, much more with support and how the software handles it.
I have recorded triple-screen (3840x1024, 30fps, audio, raw) footage whilst running a game (which loads the GPU up completely), and I could only stream that footage to a memdisk. Luckily my machine has 16GB of RAM, so I reserved 12GB as a streamdisk. I could record very very short segments (2 minutes top), but it did work.
I am not sure how fast that stream was, but probably in the order of 100MB/s. My mechanical drives top out at around 100MB/s, but soon dropoff to 60 MB/s. A modern SSD, with huge write speeds, should be able to handle that.
(note: not any SSD though, my 3 year old OCZ Vertex 2 has a sequential write speed of 60MB/s maximum - a bit more if the data is very compressible).
IMHO if their camera requires you to get a i7 and gaming GPU, they better be paying for that machine as well. Because it's out of this world you need such a machine for what is in essence a USB3.0 Full HD webcam.
Maybe hacking a HDMI Ethernet Extender instead is an option:
http://hackaday.com/2014/01/25/reverse-engineering-an-hdmi-extender/That box encodes frames to JPEG and multicasts them over UDP on the network. You can easily join as a PC (if you reverse engineer the ethernet stream to ofcourse..) on that UDP multicast group and sniff the image data. Then it's probably a little tweaking to stream the images together to a videostream and overlay a (good) audio source.