Reaction: a program that reads a camera and reacts to some user action instantly moving a robot arm. Add to that an ultra-slow-motion camera so we can see what happened afterwards.
So a computer built 50 years ago is already fast enough to pass your instant-reaction test. (Well, admittedly, maybe it didn't respond instantly, but if it could catch a thrown ping pong ball, it was probably pretty quick).
This comment isn't meant to scoff at your suggestion -- far from it -- I think an instant-reaction-bot will still impress most people (and rightfully so). I just wonder if we, as programmers and scientists and engineers, haven't been taking as much advantage of Moore' law as we ought to.
Also I saw some news about a spanish uni developing one robot arm to catch space debris.
The thing is we still don't realize how fast they really are. We say all the time that computers are dumb. The perception is somewhat distorted for most people.
Moore's law has been almost completely eaten by the screen growth. That's the easiest least imaginative way.