What _do_ they require?

They require identifying all the interaction paths that a user can take through the application so that any function associated with an interaction can correctly update the state of the application's data model. Vanilla JS, HTML, and CSS.

Do you think that's feasible for a website like Facebook? It seems like it would be much more difficult than using a framework.

Developers that have experience creating native applications are used to writing code that manages the application state and it's relation to UI interactions and data updates. In native-land, the UI frameworks are primarily the UI widgets and all of the application logic is written by the application developers in their chosen language. The corollary to this for web development is that HTML and maybe a few specialized graphics libraries like D3.js provide the UI thingies and the application logic (event handling, data fetching, etc.) is written in Javascript.

I'm not familiar with the Facebook website but I can't imagine that it needs any particularly complex application logic under the hood.

Why would it not be possible? What cant you do with js that other fancy frameworks can?

I didn't say not possible, I said feasible.

Pretty much anything is possible given enough time, but spending time building a complex application in vanilla JS, HTML and CSS doesn't seem like the most productive use of time when you can leverage a framework.