Ouch. That's going to leave a mark! The article quotes some guy as saying the pier was tough to get at as it is "thick, old wood". Kinda, sorta, but no. I was one of the assistant project managers for the construction manager when South Street Seaport was going up in the early 80's and was involved with the pier's wooden deck construction. So the wood is old, as in the tree was old, but the lumber wasn't exactly ancient.
The wood that was selected for the deck on top of the concrete pier was Bongossi, an African hardwood with some very exceptional properties. It is extremely hard, extremely durable, extremely resistant to rot, and almost a fireproof wood, which were the main reasons it was chosen for use at the Seaport. http://www.interwood.it/inglese/azobe.php
I think I still have one of the original samples of the wood that was submitted for testing and architectural approval in the garage somewhere. At the time I found it rather hard to believe that a wood could be that resistant to catching fire, but after holding a lighter flame against it for minutes at a time with little apparent effect, I had to admit the stuff really didn't burn readily. Of course my simple test was done on a piece of relatively freshly cut wood, and not a piece that had been exposed for a few decades, but there is little doubt that Bongossi is a very special wood indeed. Once the decision was made to have a wooden pier deck, Bongossi was about the only real choice.
For that wood to have caught fire there must have been a concealed fire burning for some time. A lit cigarette by itself would not have done it. I can only hazard a guess that maybe a cigarette ignited some debris that was between the deck and the concrete pier, and that the fire must have smouldered for a while before the deck went up in flames. I'm just glad no one was hurt.