Launcher does not update game location correctly

When moving the game from program files to another location, I noticed that some launcher features still think the game is located in program files. This also happened after restarting the launcher. The game starts fine.
I noticed this with installing content from the OpenRCT.net Store and the 'Install Steam Stub' option.

No files or tests are named. Start by reproducing the issue after moving the game and restarting the launcher, then trace how the OpenRCT.net Store and “Install Steam Stub” features resolve the game location. Done means both features use the moved location consistently after a restart.

Written by the indexing model from the issue text.