My issue now is that that I have misunderstood the nature of the DisplayPorts on my computer.
I suspected that from reading your post that's why expanded on that topic.
I have a PC that I built for shows. In my GTX980 I have 3 Displayports and an HDMI port. Based on what your saying I won't be able to take input through these ports, which I was starting to suspect before I read this. My computer does not have thunderbolt ports.
Correct!
Does this mean that my Displayports work as a PCI-E port?
No but some motherboards can take a Thunderbolt adapter and you would connect your GPU to the TB adapter to combine DisplayPort and PCIe on the Thunderbolt pipeline.
Is there such a thing as a USB capture device?
Yes but you'll need USB3 to get HD. My recommendation would be to buy a PCIe capture card assuming you have room on your motherboard. My favorite card at the moment is a Blackmagic Design Duo 2 card which gives you the flexibility of having 2 Inputs/Outputs or or any combination of 4 Inputs/Outputs. (3/1, 1/3, 2/2, 0/4, & 4/0) but there are many cards on the market that can give you various options such as 4K, HDMI, Component, etc...