Generally I assume that they ran the red light because they didn't see it. That's the only time I've ever run a red light. Honking the horn serves two purposes:

1) telling the runner to wake the hell up and pay attention; if they're asleep enough to run through a red light, who knows what they're going to hit/etc next? I appreciated the honks the two times in my life that I've run red lights.

2) Heads-up to everyone else around that there's something wildly dangerous going on, look out.

"Disciplining" the other driver isn't the goal.