I suspect he uses both 120VAC and 12VDC - the first to provide a clock reference, and the second to power the circuitry. It wouldn't be hard to wire in the 120VAC connection in addition to having a 12VDC adapter.
This reminds me of a very interesting challenge on smashthestack.org (IO #11 I believe), involving creating two brainfuck programs with the same MD5 hash, which produced quite different outputs. Excellent learning process. Having this article probably would have cut a week off the time it took to complete...