To answer your Question:
1: you can not plug the video plugs into a PC monitor unless it has composit plugs. (not likely unless it's a LCD TV)
2: you can buy a converter to convert the composit video to VGA for $60-$100 or more. I havn't heard of anyone doing this because it's not worth the money for what you get...
Options...Use a PC and run mame on your PC monitor or spend $0 - $20 on a used TV for your Jakks unit.