from the FAQs [thanks bZkindle]
23. I have a subscription to The New York Times on my Kindle, Nook or other e-reader. Does this give me access to NYTimes.com?
No. At this time, we're not able to connect your e-reader subscription to an NYTimes.com subscription. Each must be purchased separately.
We plan to enhance our e-reader subscription options in the near future. Please make sure your e-mail address is up-to-date so you can receive the latest site news and announcements from NYTimes.com.