Symptoms

As K2 Task List application exist for Windows Phone 8 you may expect the same be available for Windows 8 desktops and laptops.
 

Diagnoses

K2 currently has K2 Worklist preview app available in Windows Store:
http://apps.microsoft.com/windows/en-us/app/k2-worklist-preview/85f8a6fd-86bf-4fef-bbae-6486b10a2c24
It works on Windows 8.1 Enterprise and Pro. This preview app will be replaced with a universal K2 Mobile app which will support Windows 8.1 and higher. This app should be available later this year.
None of these apps will work on Windows 8.0.
 

Resolution

There is no such app for Windows 8.0, but you may expect K2 universal Mobile app to support Widows 8.1 Pro and Windows 8.1 Enterprise, once it will be released this year.