It is really odd why does not work with Windows 8, because on the Waypoint Q&A it say's that it is compatible.
Halo 4 SmartGlass activity displays an error reading “Your device is missing certain required features.”
This error will occur when using the Halo 4 SmartGlass activity on a Windows Phone 7.5 or Android phone. The Halo 4 activity is not compatible with these devices. The list of compatible devices is:
Windows Phone 8