You don't have to read the newspaper for it to influence your your life, or even your own opinions. The institution has enormous power. Your example, the NYT,

You don't have to read the newspaper for it to influence your your life, or even your own opinions. The institution has enormous power. Your example, the NYT, is quoted on TV and radio every single day, in and out of the US. Add to that the number of private who quote, forward, regurgitate-as-if-they-thought-of-it the articles. The power of the mainstream media is waning, but it is still more significant than anything else, other parts of the Internet included, in swaying voters.