I found a solution to this problem that LucasArts obviously doesn't want anyone to know about (concerned that people with Admin privileges might screw up their registries).
This is not a workaround, it actually solves the problem.
Please only do this if you are comfortable making changes to the registry. If this is done properly, no harm can be done, but I will not take any responsibility if this causes anyone problems.
I don't know why LucasArts chose to not let users other than the Administrator play the game. I can understand that the permission to install the software should be blocked to anyone other than the Admin, but for security's sake, other users should be allowed to play the game.
IMPORTANT
Please note, you have to be in posession of Administrator privileges to install the software, and also to apply the change to the registry explained below. You should know what you are doing, if not, you better not do anything.
And another thing: trying to install the game will fail- the game will install, but an error message will make you aware that registry keys could not be created. Also, trying to start the game (without having applied the change to the registry explained below) as any other user other than a user with Admin privileges will result in corruption of the games' files, even if an Administrator has installed the game.
Ok, enough warnings, here goes:
The game creates a key in the registry of Windows 2000.
This is the location and name of the key:
HKEY_LOCAL_MACHINE/ SOFTWARE/LucasArts Entertainment Company LLC/ Monkey4/ Retail
This key contains a bunch of values. But believe it or not, nothing in the registry needs to be changed. It is the permissions for the keys that need to be changed a bit. Because as it is, only user accounts with Admin privileges can give the game proper access to check and change the registry key(s).
Let's assume, for the sake of this explanation, that you want the user "robot", who is a member of the "power users" group, to be able to play the game.
To do that, open regedt32.exe and locate the "LucasArts Entertainment LLC" key. Go to the menu bar and click on "Security". Then click on "permissions..."
From the list of user groups that is presented, choose the "power users" group. In the field below the list of the user groups, there are two check boxes. Put a checkmark in "Full Control". Oh yeah, make sure there is a checkmark in the box next to "Allow inheritable permissions from parent to propagate to this object". To finish, hit "apply", then "OK". Now exit the registry editor. Log in as "robot", and play the monkey Island game!
That's it! What you have done is you've changed the permission to access and change the Monkey4 registry Key (and the two sub-keys)! The permission was extended to the user group "power users". That means, all users of the group "power users" are able to play the game.
Have fun.