They have exclusive rights to it, or he should do it as a courtesy?
Yes and yes. It's one thing to put up some clips. It's another to do a fully edited video story. I haven't asked nor heard whether the clip of Avery's final putt was removed because someone asked. It could easily have been a rep for Avery that asked it be removed, not the PDGA or Media Active (Worlds DVD producer), since there's also a Jenkins video being prepared for eventual sale.
What exactly is it that gives the PDGA exclusive right to footage of this event?
Before I start, I would like to say that I have never been to Worlds, so I don't know how these things are run and they are genuine questions.
This event is held in a public park, where spectators are welcome. As far as I can tell tickets aren't sold to spectators, you can simply show up and watch (if I am wrong it would make a difference). Does the PDGA pay for the exclusive use of these parks during the event? Are there signs up during the event prohibiting videography/photography? Are spectators allowed to use photography equipment during the event?
Since there is video and photography from these events, I am assuming that spectators are allowed to have photographic equipment at the event. Barring signed waivers (or signs at the event), I do not believe that the PDGA can legally claim exclusive rights to publishing video. And while the PDGA may think it is one thing to put up some clips vs a fully edited piece, I do not think this is actually the case. (though if the PDGA can actually make an exclusivity claim, then they could just look the other way for short clips).
p.s. - my background is in photojournalism, so if I am coming off harsh it is just me being a little defensive in an era where events are increasing stealing the rights of photographers to their images (I am not accusing the PDGA of this)