It's not. It's just crazy to think that a web app with $0 revenue that's been around for ~2 years can be worth a newspaper that's been around for over 150 years and has won more Pulitzer Prizes than any other news group.
It seems crazy but it isn't really. What if NYT has a lot of debts? It could be worth negative amounts, since the new owner could be responsible for those debts.
There are plenty of ways for a large company (especially an older company) to have a neutral or negative market cap, since that is based on its profit potential, not on how much economic activity it creates.