I am a product manager for the Eventbrite API, so hopefully I can help you out.
The Calendar that you're showing is an integration that was built for the WordPress.com platform, and isn't available elsewhere.
There is an open source library for .NET which you might find helpful: https://github.com/penguinboy/Eventbrite.NET
Alternatively, Eventbrite does have a calendar widget that can be plugged into any website: http://developer.eventbrite.com/doc/widgets/#calendar
Hope that helps!