If only one monitor is working in your setup you might be missing the second video connection. Two video connections are necessary for both computers to receive video, a single video connection cannot be split/extended. 

USB C | Thunderbolt | DisplayPort Alt Mode

To make the second video connection you can looks at the available ports on your computer. USB-C ports with Thunderbolt or DisplayPort Alt Mode may be available on your computer, these ports can support video via a USB-C to HDMI adapter. 

Mini DisplayPort

Some Laptops may have mini DisplayPort available. This is a smaller version of DisplayPort that can support high resolutions. You can use a MiniDP to HDMI Adapter. 

VGA

Less common on modern computers but still some come equipped with VGA ports. Supports lower resolutions typically up to 1920x1080. You can use a VGA to HDMI Adapter.  

USB 3.0

If you don't have any of the ports mentioned above you might have a USB 3.0 on your computer that can support video. Looks like a regular USB-A port with blue. A USB 3.0 to HDMI Adapter will be necessary (drivers are necessary, not compatible with Mac OS)  

Once you have both video connections you should see both monitors receive a video signal and your good to go. To have a better understanding of how the KVM Works check out the image below. On the input side of the KVM you have "HDMI A" & "HDMI B" these HDMI inputs send the video signal over to the monitor outputs of the KVM. "HDMI A" sends video to "Output A", "HDMI B" sends video to "Output B"