There are VGA to HDMI upscaler boxes that are relatively cheap. My guess is that is probably what he will be using.
Hey guys here's what Im using for the game capture device Im using the Elgato Game capture HD, but you need to also get from the Elgato sight a cable that is for composite hook ups, the pack in cable will not work you have to get that special one. The Jaguar plugs right into that set up no problem - but the Lynx has a few more hoops to jump through. The VGA out on the Lynx goes into the Enjoy Gadgets EGVGA RCA generic PC to TV converter. Then I capture the audio with a phono to RCA cable into the Elgato. If you guys would like I can do a video on the set up, that might be cool.