He came into office in '70, and the coup was in '73. From the very link you posted: "29th President of Chile In office 4 November 1970 – 11 September 1973." What CIA planned doesn't take precedence over what actually happened.
On May 26, 1973, the Supreme Court of Chile unanimously denounced the Allende government's disruption of the legality of the nation in its failure to uphold judicial decisions, because of its continual refusal to permit police execution of judicial decisions contrary to the government's own measures.
Could it be possible that the CIA wanted to remove him as soon as he got elected AND that also and independently he abused power so much as to lead to this declaration by the supreme court?
I tend to respect each country legislative body - especially at the higher level. More recently, even Zimbabwe supremes denounced the abuse until they resigned - see http://news.bbc.co.uk/2/hi/africa/1850771.stm