Was the runway upgrade at Mataveri Airport on Easter Island really related to the Lee Correy novel "Shuttle Down"?
As much as I enjoyed reading the novel after reading the Wikipedia article about Mataveri Airport I am somewhat disappointed by my answer. The novel was published in 1980 and the official agreement between the United States and Chile was not signed until 1985 there is circumstantial evidence that the novel did not play a causal role. 

In Glynn S. Lunney's Oral History from NASA's Oral History Project. Link to Full Text It appears that from very early on in the Air Force's involvement with the Shuttle Project that Easter Island was identified as a possible abort landing site. They didn't like it because of the short runway but they thought about it. Because this is an oral history it is hard to pin down exactly when these thoughts were happening but the context makes it look like it was quite early. 

Naturally all of the news articles from 1984-1987 about the extension I found never mention the novel. Nor does the official text of the Agreement. 

It was a fun little novel though. Which strangely enough foresaw most of the logistical problems that would arise from having a NASA retrieval crew on Easter Island. Especially the water and sanitation limits. 

Having kept looking for a bit I found an interesting declassified memo from 1966! The Air Force has been considered their own manned space flight program launching from the Western Test Range heading south and using Easter Island as a possible abort landing sight. Another memo from 1967 says it got so far as actual discussions with the Chilean government. Even though these documents were classified it is clear that the idea of using Easter Island as an emergency landing site did not come from the novel.