That longer clip shows he was pretty determined, nearly had it too. shame the guy behind didn't at least run over the bike he'd dropped.
I wouldn't have. If you get a spoke through your tyre, you'd be vulnerable to attack by a pretty brazen criminal.
What I would have done, however, is lent on the horn and blasted it until everyone one on the street was staring and the thief (oh, "cyclist") had fled the scene, not some polite "pip" after several attempts.
Edit: I watched it again, and the following driver does let the horn blast. It's after the bike would have already been stolen if the thief had twisted the knob enough times, but in fairness, it might take a little while to realise what you are witnessing and react. We have a better view than the following driver.