I use a Limited User Account ("Standard User" on Windows 7). In the past, I have discovered that many games - apart from those made by Electronic Arts - usually require Administrator privileges; not only during the installation, but also just to play.
Wing Commander also appears to require Administrator privileges just to play.
On some games, I can usually solve this problem by giving "Modify and Write" permissions for the "Users" group to the game's program folder (C:\Program Files\*Game Folder*). In some cases, I also have to adjust the permissions in the registry; nightmare.
I have gave Wing Commander's game folder "Modify and Write" permissions - and now the game starts and appears to be working just fine from a normal "User" account. So I just thought I should post this here in case there is anyone who would like to run the game without Administrator privileges.