As far as technology goes, the NYT site is built on the Foundation framework. The interactive graphics are based on D3.js. There'll be a bunch of data analysis, database skills, design, HTML, CSS, JS, etc in there as well.
But... if you want to build something similar, learn team skills. A site like that isn't built by an individual.
Yes, I am being cynical - but I cannot extract any information from the "article" because on my FF on OSX any attempt at scrolling leads to seemingly random stuff changing without any option left for me to read it sequentially.
I agree with you completely, with a finance background I still stared at it for a while and extracted very little.
Its all there, but I had to do my own 'analytics'.
But... if you want to build something similar, learn team skills. A site like that isn't built by an individual.