Most of the stock is family owned...there is no real and open market around the Times.
Adolf Ochs (who acquired the Times in 1896) wanted to ensure that his family would always control the organization, so he created two classes of stock: the publicly traded Class A, and the family owned (and not publicly traded) Class B.
The Class B investors elect 9 of the 14 members of the NY Times board of directors, effectively giving them control of the organization.
Ochs was an interesting fellow. Part of his success was the observation that newspapers in the late 1800s were openly partisan. He felt people would appreciate an objective source of the news, and this was his philosophy with the Times.
I imagine he is rolling over in his grave...