I figured I'd only have to register the newest one, since it overides all the older add-ons/patches/original game. So, to get a beta for a game I already have registered, I must register an earlier game which the beta patch isn't even meant for...
Groan! Where did I put that EU3 Complete box...
It's not a new game though, it's an expansion which requires the original game. I suppose the logic is you may have 0, 1, 2 or 3 expansions, but to be playing anything you must have EUIII, hence why it's the one they check for.
Another reason would be expansions tend to be cheaper than full games, so if you were someone who'd pirated the game but then wanted access to the betas, if it were allowed the cheapest method would be to just buy and register an expansion. I'm aware that's not the case with EUIII and HttT due to how old EUIII is, but I would imagine when you are running a forum with dozens of different games you'd want to set up some basic rules for registration, not go through each one on a case by case basis.