On linux, whether it's Chrome or Firefox, none of the videos play. Really great experience but would love to see the videos. When I get home, I'll have to pop open my Mac to get the full experience.
I had this issue but noticed it's because the Ghostery chrome extension blocks Brightcove, where the videos are hosted. Maybe you have a similar problem?
I also had this issue, in my case the culprit was the Kill-Flash extension. Adding nytimes.com and brightcove.com to the whitelist made everything work.