A run by Mr. Feinblatt would complicate what is already a three-person race because he most likely would have the support of the powerful mayor, who is running for a third term. Such a move could also irritate the outgoing district attorney, Robert M. Morgenthau, because it could hurt the chances of his preferred candidate, Cyrus R. Vance Jr. The relationship between Mr. Morgenthau and Mr. Bloomberg has been strained, in part because of the district attorney's investigation into the fire at the former Deutsche Bank building, which found that lapses by the city had contributed to the deaths of two firefighters.
Mr. Feinblatt does not intend to run this term. Robert M. Morgenthau, Cyrus R. Vance Jr. and Mr. Bloomberg do plan tto run.
There is no statement of intention to run in the original passage, just predictions of relationships which will be effected if one person does. 'would' doesn't mean 'will', perhaps the AI doesn't know this?