This is a link to how the licensing page appears on the customer who has a production license

http://www.k2underground.com/members/BasharA/files/K2License.bmp.aspx 

Maybe I'm not understanding your question correctly.  However, the screenshot you showed is what I expected for a production system.  There would be no expiry date on actual purchased K2 licenses for development, staging and production.  As far as I'm aware the only K2 licenses which expire are on evaluation and partner licenses.

So there is no expiration for production servers.

This raises a question... How does k2 benefit from selling their product if there is no update for the license key?

Since that particular customer already has a production key K2 must have already sold the customer the K2 licenses.  Customers that want access to the latest versions, updates and support also pay an annual maintenance fee.

Thanks for the clarification