The issue appears to be that in the case of MinigameMadness, the project is no longer blueprint only.
In the broken case:
ProjectGameExeFilename=C:\Users\Enrico\Documents\Unreal Projects\MinigameMadness\Binaries\Win64\MinigameMadness.exe
In the working case:
ProjectGameExeFilename=C:\Program Files\Epic Games\4.10\Engine\Binaries\Win64\UE4Game.exe
Did you recently make any changes to the uproject that might have made it a code project?
Your VS2015 install is still not working, and it looks like there is some problem with the 2013 install as well. Those issues are likely independent of your engine version change.