My memory could be failing me, but pageants I believe pageants I’ve seen in the past have been as described in the article: announce 3rd, then announce 2nd, the winner remains.
I don’t know if this is what they intended, but Mr. Harvey did it as you described. It’s strange, because he mentions that the 1st-runner-up will fulfill the duties of being the winner, should the winner be unable to. Then, he goes on to call the name next to “1st runner-up” as the winner.
I still think it’s good to have all three names up on the card. This is what I would describe as “error prevention.” You can verify that yes, in fact, the remaining person is the winner (or 1st runner-up, depending upon how you look at it).
But, this all depends upon the emcee reading the card correctly, and being aware of the protocol. Neither of these things happened in this case, and I’m not convinced having two names would have made that any better.