Well, it was intended to be amusing, yes. (In retrospect, perhaps "if there was more than one of it, it would be a multiplicity" might have worked better. Perhaps not.)
That said, I do think there's an actual point buried in there somewhere. The sorts of people who use the term "Singularity" to describe an event are deliberately using a term that isn't commonly used to describe transition points, precisely in order to convey the inadequacy of former transition points as a reference class for thinking about that event. If "singularity" were a word in common usage to refer to other transition points in history, singularitarians would choose a different word.
Yes, I think you're right, concerning contemporary usage; but it's not clear to me that either Ulam or Vinge had that connotation in mind.
ETA: Or von Neumann.
If you have graphic design experience, check out the on-going logo design competition at 99designs for the Singularity Institute. There are still 6 days left to enter and be eligible to win the $295 prize if your design is selected. Tell your friends with graphic design experience too. There are very few submissions currently.
Note: This is a blind contest. Designers can only see their own entries. All designs will be revealed when the contest ends.
If you're interested at getting a peek at the designs, they will be online after the competition is over. This is standard practice in 99designs contests to prevent designers from contaminating each other and having all the designs drift in a certain direction.