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.
That's not my experience with Chrome on Linux; everything worked.
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.
Works fine for me in Chrome and Firefox on Xubuntu.
The videos on both Firefox 17 and Chrome 24 worked for me on Linux.
Looking good here ... Squeeze 64, KDE, nVidia GTX 570 ...