When clicking on the icons of the first three games which are supposed to come bundled with the game, I only get the "help" section of this page but can't get any of the games started.
Any ideas?

Run them outside the game?

This is the correct answer, it most likely will never work unless the devs fix it. I dove into this issue yesterday and from what I can gather the Apple IIgs emulator that is used to run the original trilogy is probably looking for files/libraries related to the X Window System. Specifically KEGS looks for the X11R6 directory which modern distros no longer have. It would probably be a relatively easy fix if you could access the source code and update some things. Gsplus which is based off KEGS works well on my machine and that's what I have been using to play the original trilogy.