Do you (Gog) think that you could maybe remove the administrator requirements from your install files? On my parents computer (I don't have net access at my house), they're really anal about forking over admin privilages, and they've stuck me with the guest account. So I've no way of playing the games that I bought! :' ( Maybe? Just this once? For me?

Admin requirements is a standard for installations on a PC.
I have no idea of what it'd involve, but I'm sure modifying the install code of every game you've bought would be tedious. It'd be easier getting your parents to allow you to install the programs than disabling admin prompt, of that I'm sure.
You could also always buy yourself a cheap laptop and install them on that.

See, but I've bought and installed games without admin privaleges on this pc. Like, for example, the steam version of Half-Life. And I've downloaded and installed Beneath a Steel Sky from other websites and installed it just fine.

Wait wait wait. You have your own house but your parents dont trust you with admin access on their pc? How do they trust you to lock your own door and put yourself to bed on your own?
oh and why dont you just download the file stick it on a disc then just take it home and install it? or do you spend alot of time at you parents?

or a cheapo flash drive, seriously..
Also: computers are weird magic devices that cost a lot of money.

I don't know Steam intimately, but from what I understand a portion of Steam runs in the background (as a service) which has administrator rights. When you installed Half-Life the service with admin rights may have been doing the actual installation. Others could clarify that more.
Some games/programs don't require administrator rights in order to install or run, particularly anything that uses DOSBox or ScummVM. In those cases the installer would default to installer under Program Files and in other cases would likely default to the user's profile.
If your game uses DOSBox or ScummVM, you can probably unpack it and run it from the extracted files. Not the easiest method, but if you can't convince your parents to grant you access to an admin account (only for installing, not actually running the games) it can be a useful approach.

If your parents are that bad about it, then just right-click on the installer and choose the "Run as..." option. Pick one of the admin accounts, let them enter their password and it will install. AFAIK, you don't need admin permissions to actually run the games once they are installed.
Frankly, the solution here is not for GOG to change anything when the problem is not how they made the installer, but rather it is trust issues between you and your parents... that and you need to get your own PC. If money is a problem, then perhaps your focus shouldn't be on getting games but instead saving up to afford a PC.

You're close: Steam changes its folder permissions so that all users have write access to it (even if it is in Program Files). This means that Steam games can be installed and updated by any user without any UAC prompts (except for games that need to install DRM or other special components). This nasty workaround is a potential security hole and completely ignores Microsoft's design security guidelines (which UAC was meant to help enforce in the first place), but Valve seems content to continue using it.

Also if I'm not mistaken don't you need admin rights to install steam in the first place?

Gog could make the game install in a folder that the guest account does have write access to or it could just install to the public folder.

But why do that when 99.9% of all software is installed in exactly (or nearly exactly) the same way that the GOG installers work? There is no reason for GOG to make a non-standard installer for the incredibly rare situation like this, where the problem is not really on GOG's side at all, it's on the user's side. Besides, modifying the installer like that could be considered a violation of security "best practices" which is not something you really should do on Windows anyway; it already violates enough security practices on its own.

Some programs install into your user account, Google Chrome for one does this (though I forget if it asks for admin rights anyway), but I guess that wouldn't work with a guest account anyway instead requiring at least a "normal" user account.

Nope, guests don't have write access to the necessary parts of the registry, only admins do I believe. Also, the installer tries to launch an admin process before you get to choose an install path.

Ah, okay. The only options then would be to extract the files without executing the installer, or to install on a different computer and copy the files on a flash drive. (As earlier posters suggested) This wouldn't work for all games though, some might for example require certain registry settings in order to function.