The game's installation folder is where the game's files are stored, displayed as <path-to-game>. Save files are sometimes stored here as well but many newer games will put them in a different location.
The Steam folder contains data for games using Steam integration; it uses the following locations by default:
Game data is saved within a folder called steamapps found within the Steam directory.
The Origin Client folder contains data for games using Origin integration; it uses the following locations by default:
The Uplay folder contains data for games using Uplay integration; it uses the following locations by default:
%PROGRAMFILES(X86)%\Ubisoft\Ubisoft Game Launcher
%PROGRAMFILES%\Ubisoft\Ubisoft Game Launcher
C:\Documents and Settings\(Username)\
C:\Documents and Settings\(Username)\Application Data\
C:\Documents and Settings\(Username)\Local Settings\Application Data\
C:\Documents and Settings\All Users\
C:\Documents and Settings\All Users\Application Data\
A User ID is a unique identifier used to identify accounts. Files are sometimes saved to user specific location such as using profile name or numbered ID in filename/path indicated by <user-id>. This can vary between users.
Note: The hidden Library folder can be reached via "Finder > ⇧ Shift+⌘ Command+G > ~/Library > Go" path.
Note: a game using the fall-back paths doesn't guarantee it is following the XDG specification. For example, Game Maker and Unity 4 titles do not actually use the relevant environmental variables, despite using the correct fall-back path.