The Intercept and Quartz each only publish a few articles per day. Each runs entirely on a single instance of Wordpress. Each covers only a few topics. Each has only a few templates, and simple ad inventory, if any.
A paper like the New York Times publishes many hundreds of stories every day, on almost every topic you can think of. They publish to wide variety of platforms, including print. They have a high volume of widely varying ad inventory. They have legacy content going back decades, in all sorts of legacy formats, perhaps even sitting in old CMS instances on separate servers.
TECHNOLOGICALLY SPEAKING, they are much more complex. Therefore transitioning to HTTPS is more difficult.
None of this is a commentary on the quality or social/cultural value of their content.