Some time ago, Microsoft replaced the Skype UWP app with a newer electron version in the Store. Due to this update, Skype lost some of its features, which Microsoft is now restoring in the latest app version.
The transition from UWP to Electron was not smooth, but it allows developers to easily adapt Skype for more platforms, such as Chrome OS.
A new release of the Skype Store app now allows you to answer to chat messages directly from desktop notifications in Windows 10.
The feature was previously available in the UWP app, and not it is enabled for Insiders. It should also reach the stable branch in the near future.
Source: Florian B.