My friend built his first arcade "machine" as a portable control panel. Indeed he shoved a computer in there and on the back simply had a vga out, svideo out, and a power cable. Just plug the video into either a TV or Computer and plug the power in and you're ready to go.
As far as "portable", well he used a standard sized motherboard and power supply. So it was about a foot and half tall and 3 or 4 feet wide. He attached handles onto the side so that he could carry the thing about.
He ended up ditching the idea and rigging the control panel face onto an old arcade cabinet.
The thing was so popular that friends were demanding that he leave it at their house on loan. And everytime it seemed like somebody messed something up. Whether it was snapping a wire, or messing up the MAME or MAMEWAH settings, or even Windows. he was just kind of sick of having to trouble shoot it.
So, after seeing my cabinet, he decided that an upright would save him from the guilt of having something that's portable enough to loan out but not wanting to loan it out.

Also, the box was a bit heavy and he was kind of tired of lugging it out and back to "storage" everytime he wanted to play. He was kind of looking for an excuse to leave his "arcade" in the living room all the time - rather than plopping it down on the floor in front of the TV each time.
Joseph Elwell.