Given that the data for the first few years result from a small number of pages, the graph doesn't allow to reliably distinguish between both interpretations, and his (and your) interpretation is not really justified. If you look just at the complete, reliable years (links from 2000 to 2010), the graph looks convex, just like you'd expect for exponential decay but not for linear decay. So while the first interpratation is probably intended by the author, I'd say he is overstating his case and is most probably wrong.
Yes, indeed. That is a nice graph, and in absence of a mechanism that would explain why no link can last longer than 28 years it should quite convincingly show that linear decay has not been established.