HDMI Capture Card
This "cheap" HDMI capture card from Amazon and Ebay may look like a sub par, sub quality capture card. I've seen prices range from 10 bucks to 30+ for the same device, so do a little digging and find a price that suits your budget.
The device is plug and play with modern systems. I tested this on a 2007, & 2009 iMac, a 2012 Macbook Air, and a 2015 Dell XPS 13. All picked up the device with no issues.
Another perk of sorts, is that the device itself is about the size of an USB flash drive. So it's easy to carry with you if that is needed, and while USB 2.0 it does not require external power to operate. The specs calm it can capture at 4k resolutions, but will only output to your computer at best 1080p. I know I know... 4k 8k is all the new shiny super awesomeness (and it really is... but I can't justify that cost). For what I do, right now... 1080p is a great starting point.
I've tested it so far with a couple of different cameras as "webcams" of sorts to the iMacs. I tested a Go Pro Hero 2 (old I know...) and a Canon Eos Rebel t3i. Both were captured with little fuss. Photobooth and Quicktime Player (set to make new video).
For the 10 bucks I paid, I'm not remotely upset at the performance. It just works. If I encounter issues, it's usually due to the limitation of the system I have it connected to and a quick restart has fixed them.
As always, please post any questions or comments below and I'll respond as best as I can. Thanks!
Photos of the device are below: