Well more to the point, how do I take advantage of GOG's maintenance without installation? (I don't have admin rights on this computer)

I can unpack them using innounp, mount them and run them just fine, but they just don't work very well. They either:

A: Run very slowly (Blake Stone, Might and Magic 1-5)

B: Mouse doesn't go where I want it to (Teenagent)

C: They just don't bloody start (Earth 2140 DOS)

But I do notice that on the shortcuts of GOG's already installed there are some fancy stuff that reference some of the files GOG includes. I have tried to emulate those, but that doesn't seem to work either.

In a nutshell:

Just put the {something}.conf file in the game's directory, together with DOSBox.exe, SDL.dll and SDLnet.dll, after unpacking the package, and then make a shortcut to DOSBox.exe and give it the argument -conf {something}.conf -noconsole -exit.

You may need to do some additional modification to the {something}.conf file, but then I guess, that's what happens when you use bloat instead of making KISS packages that are guaranteed to work even if the user didn't install the package "the way we wanted them to install it".

If you need help with a particular game, let me know and I'll tell you what you need to modify in the .conf file for it to work.

EDIT: Why did GOG need to package the things the way they are packaged right now is beyond me, adding more complexity for the sake of complexity or ... wait for it... debugging reasons (what a joke, do you really need to debug an Inno Setup script that is downright obvious from the moment you look at it?).

How familiar are you with DOSBox?
DOSBox requires specific configuration files, which GOG provides for each of its games. So instead of running DOSBox itself, you have to run it with the needed config file. A few of the games (Darklands for instance) also require a few fixes on the DOSBox as well.
So, unpack the files, then re-create the shortcut, or drag and drop the .conf file to the DOSBox executable, though in that case you'll probably have to fix the paths as well.

I think we had a thread about how to turn DOSBox games into portable apps, let me go look.

Edit: I found this thread which I'm not sure how big a help it will be. But you can also follow Elenarie's instructions, which do seem simpler, and will probably work as well.