Teradici is that, but too expensive for home users.

It looks like I can find Teradici card for $50-200 (used to new), which is in a similar range as the JetKVM. However, according to the installation manual that I found [0], you still need to plug in the DisplayPort connector on the Teradici host card to the GPU output port(s).

0: https://anyware.hp.com/web-help/pcoip_remote_workstation_car...