I recently worked with getting an EasyCap device to capture and record from a projector on another input to the output of the computer with the EasyCap attached. The results were not great, but if you needed a small size video with not so great resolution, it was good for the money (EasyCaps  are around $6). The one thing with working with the EasyCap was that I found the drivers/apps that work with the EasyCap are easier to use on the Mac side. I used  free app called EasyCap Viewer. To find a driver that worked with my Easycap for the Windows side was very hit and miss and time consuming. There are sites out there for drivers but make sure you know your make and model of EasyCap before downloading it. I used a VGA converter box (very similar to this one) to take the second input and output it to the Easy Cap to capture on the computer. This converter box did cut the resolution down. Also a big tip with the VGA Converter Box, make sure you take a look at the system adjustor. It may be set to PAL (so you won’t get any picture) or one switch to NTSC and the other set to PAL (so you result in a black and white video output). I had to have one switch (it’s white on the side) up and one down to get color. All in all the EasyCap worked with the VGA converter box (we were using S video with EasyCap) but we found the quality and resolution to be less than desirable.
I hope this helps!