The problem here is that you use the same {#MyAppName} ISPP code for all 3 games. This just means that the installer actually creates all 3, but overwrites the previous because of the same shortcut name.
Change it like this
Code:
Name: "{commondesktop}\Resident Evil"; Filename: "{app}\Resident Evil\ResidentEvil.exe"; Tasks: desktopicon
Name: "{commondesktop}\Resident Evil 2 Leon"; Filename: "{app}\Resident Evil 2\LeonS.exe"; Tasks: desktopicon
Name: "{commondesktop}\Resident Evil 2 Clair"; Filename: "{app}\Resident Evil 2\ClaireS.exe"; Tasks: desktopicon
Do the same for {group} constant in [Icons] section.
PS: {group} are startmenu icons. If you don't want them you can delete them and just keep desktop shortcuts.