Is it really HDMI? If so, then you can look for an HDMI capture device that can plug into your laptop. Lots of those - standards are standards - but I would strongly advise you to not get a cheap one. Expect to spend about $100 per channel to do it right.
The cheap ones have several problems:
- Random latency. Not really sure why, but it can be anywhere from 100ms to 500ms or so, and be different every time you turn it on. If you're only recording one of them, then you're probably okay, but if you have multiple that have to stay in sync, or if you're using that to control something, it's not going to work so well.
- It may not handle all video formats equally well. I have a cheap one that takes my camcorder's 1920x1080i (interlaced, actually 540 lines per frame, not 1080, and every other frame has every other set of lines) and reports it to the host as 960x540. (Hey, at least it doesn't report it as 1920x540! 'Cause that's technically what's on the wire in that format.)
- The cheap USB ones often have a USB 3 connector and are sold as such, but they actually have a much cheaper USB 2 chip inside. Thus, they must compress, in the device itself, in order to cram it through USB 2. It's usually MJPEG compression, which is literally just a JPG of each frame as a still image with no knowledge of the other frames, so if you've seen the "JPG fuzzies" on a photograph, that's what it's doing to your video. It's not as noticeable with a camera as it is with a PowerPoint presentation or something like that, because JPG is designed specifically to blend the artifacts in with the camera noise, but it's still there.
- They're often exactly identical from the factory, *including the serial number* that it reports to the host! This is not a problem if you only have one, but if you have multiple, then it can really freak out an operating system that insists that everyone has followed the standard.