It does say "no resident", so I guess you only have to register in your home town. I haven't heard of any towns that implement this though. Actually, I haven't seen any evidence that traffic laws are enforced against bicycles at all in MA, except for the one day a year that the Cambridge PD sends out bike cops to write warnings for trivial offenses (which was yesterday, apparently).
It's definitely a weird law, though. I noticed that the fine is only $1, so maybe it's an old law that they never bothered to take off the books?