Há uma atualização do Windows lançada (hoje) que corrige esse problema.
Hotfix ( KB2902892 ) para corrigir falhas no aplicativo do Skype no Windows 8.1
When you start the Skype Windows Store app in Windows 8.1 or in Windows Server 2012 R2, the app immediately crashes, and Windows returns to the Start screen. This issue occurs when the computer uses an Intel(R) HD Graphics 3000 (Sandy Bridge) graphics device," Microsoft stated on its support page