It had been opened using an old copy of StuffIt Expander (9.0.1). That's not the way OS X normally opens zips. I used get info to view the file information, and saw that the "Open with" setting was StuffIt. I switched to the obscurely named BOMArchiveHelper -- the internal OS X application. That did the trick; the folder now had a proper widget and I installed it. I clicked the "Change All" button as well.
There's more than one problem here. As has been well described by 'Drunken Fireball' and others, Apple seriously mangled the innards of OS X when they switched from the well designed Mac Classic metadata system for data file type and creator to the kludged mixture used by OS X (way too weird to describe, it's some mix of old metadata, new metada, the three character file extension (whether hidden or not) and the phases of Venus).
The other problem is StuffIt.